For most of the 20th century, Ernst Mayr was the ornithologist. In the late 1920s - over a period of three years, Mayr studied a blistering number of bird species in New Guinea. His careful, patient and brilliant observations helped lay the foundations for the branch of biology, known as Systematics. Systematics is the study of the diversification of life forms on earth. He was one of the architects of the Great Synthesis - which from the 1920s to the 1950s combined Darwin's biology and Mendel's laws. Mayr's contributions to this achievement were to emphasize the role of Sexual Selection (SS) in evolution and to insist that the principle object of Natural Selection (NS) is the individual organism - not the gene, the cell, the trait, the organ, the group or the species.
This phrase -->"select for the phenotype"<-- is inscribed into the Synthesis, and it remains the orthodox interpretation of what the principle object of NS is. 
Mayr was sharp enough to have predicted that - once science had a good understanding of genetics, sexual selection (in a number of species) would be deemed "the dominant driver of evolution". In the last two decades or so - due to an explosion in the knowledge of genetics, the theory of sexual selection has picked-up a momentum and a salience which would have made Darwin's head spin. Recently, the sheer volume of papers written about sexual selection has come to dwarf other topics concerning evolution.
(Mayr coined the phrases "selection for reproductive success" and "selection for survival success" - because he thought that they captured the nature of these evolutionary processes more accurately than Darwin's "sexual selection" and "natural selection" does.)
As historical background for SS being suspected to play a crucial role in speciation, Darwin - writing in the Origin and the Descent - appears an amateur, enthused and winging it with his quaint descriptions of the mating interactions on the part of non-human organisms. Wildly, Darwin speculated that the presence of extreme "male ornaments" (in higher taxa of organisms) speeds-up the spinning-off of novel species. In the 1870s, Darwin did not know this to have been a feature of speciation, yet he more than dimly grasped its significance. For his "guess-work", Darwin was ridiculed. Mayr, Fisher and Dobzhansky were among his few defenders. It required over 140 years for Darwin's hypothesis to be sustained by solid, observational data. With the possible exception of Einstein, no scientist but Darwin can lay claim to such prescience and validation.
Relatively recent evidence "strongly supports" Darwin's hypothesis that sexual selection accelerates species-diversification. Fast-breeding populations of fishes in Africa have been observed to speciate within about 100 years, and processes leading to speciation are closely linked to SS.
The more exaggerated the ornaments displayed by males of a higher taxon -> the greater the females preferences for the ornaments -> the more the genetic profile of the taxon shifts due to greater differential reproductive outcomes leading to the reproductive isolation of that taxon -> the more rapidly species spin-off from that taxon [relative to closely linked taxa where males show less exaggerated ornaments]
As predicted by Mayr - in some species, SS is the dominant driver of evolution. Darwin and Mayr were correct in linking SS to speciation, but Mayr may not have fully appreciated (or accepted) how speciation occurs - as triggered by it. Geographic separation (as in allopatric speciation) - where a daughter population breaks-off from a parent population is not involved. Speciation in Tropheus (Cichlids) was observed to take place within a population's habitat, i.e. sympatrically. On many occasions, Mayr rejected sympatric speciation - outright. 
Mayr devised a theory: peripatric speciation. He postulated that geographic separation, a decline in genetic variation and small population size are essential components for novel species to emerge. Under peripatric speciation, the "founder effect" (genetic drift in a daughter population which occurs after splitting from the parent population) is a crucial feature, leading to the appearance of new species. Mayr predicted that the genetic profile of the daughter would differ radically from its parent and that local selection pressures would favor homozygous individuals of the daughter population. His theory has been subject to numerous experimental tests, but results have not confirmed it.
Mayr contributed to the development of the Biological Species Concept (BSC). Originally devised by Dobzhansky in 1937 to describe when speciation occurs, the BSC is widely accepted as the operational criterion for classifying organisms as members of the same species - on the basis of their actually or potentially interbreeding. Mayr amended Dobzhansky's definition throughout the 20th century. He insisted that Dobzhansky's use of it was too restrictive, because it referred only to a latter stage of an evolutionary process - speciation, rather than being the description of a species as a (discrete) population. 
Mayr crafted the definition of species that is (for good or ill) generally accepted as the BSC:
Mayr later altered this definition to include an ecological aspect. He became interested in "ecological niche specialization" to help explain the level of the observed species-diversity in nature. Mayr: "... a reproductive community of populations (reproductively isolated from others) that occupies a specific niche in nature."
On an historical note, Darwin rejected that the term "species" referred to a "fundamental category of biological organisation". He regarded the application of the term "species" as a means to "arbitrarily" classify a set of organisms - which closely resemble each other.
Against Darwin and since the Synthesis (around the late 1930s), species have been elevated to concete entities of evolutionary significance. However - given all of the problems and contradictions involved in isolating species with the BSC, I'll wager that Darwin was right - yet again.
Mayr rejected that species were objects of selection, favoring the term "species replacement" - while Darwin (though he vacillated) held out the possibility that species selection had occurred.
The criteria, given in textbooks, for species selection is as follows: (1) adaptive radiation (2) mass extinction (3) key innovation(s) and (4) body size. The classic case for species selection is that ~66Myr ago dinosaur species were wiped-out but mammal species survived and proliferated. The term, "key innovation(s)" (3), is problematic, but key innovation(s) are generally described as "aspects of organismal phenotype that promote diversification" - which further the "success" of the taxa originating the novel traits. (However, I suspect that - when scientists lay down criteria as above then dicker about them semantically, they are heading down the wrong path.)
(2) From The Origin of the Species
"Every slight modification, which in the course of ages chanced to arise, and which in any way favoured the individuals of any of the species, by better adapting them to their altered conditions, would tend to be preserved; and natural selection would thus have free scope for the work of improvement." -- Darwin
From What evolution is
"The idea that a few people have about the gene being the target of selection is completely impractical; a gene is never visible to natural selection, and in the genotype, it is always in the context with other genes, and the interaction with those other genes make a particular gene either more favorable or less favorable. In fact, Dobzhanksy, for instance, worked quite a bit on so-called lethal chromosomes which are highly successful in one combination, and lethal in another. Therefore people like Dawkins in England who still think the gene is the target of selection are evidently wrong." -- Mayr
"The two belief systems [differing positions held by geneticists and naturalists] had only one inconsistency--the object of natural selection. For the geneticists the object of selection had been the gene since the 1920s, but for most naturalists it was the individual."
"Elliot Sober showed how one could resolve this conflict. He pointed out that one must discriminate between selection of an object and selection for an object. The answer to the question of what is being selected for specifies the particular properties for which a given object of selection is favored. However, a particular gene can favor an individual without being the object of selection because it gives properties to the individual that favor its selection. It is a selection for these properties." -- Mayr
"An adaptive trait is an aspect of the developmental pattern of the organism which enables or enhances the probability of that organism surviving and reproducing in its environment." ["Genetics of natural populations XXV. Genetic changes in populations of Drosophila pseudoobscura and Drosphila persimilis in some locations in California". Evolution 10 (1): 82-92.] -- Dobzhansky (1956)
"No matter how much power Dawkins wishes to assign to genes, there is one thing that he cannot give them - direct visibility to natural selection". -- Gould
Also, see: "Sexual selection in Tropheus":
"The rapid rate of cichlid speciation is explained by Darwin's theory of sexual selection and the evolution of apparently "maladaptive" traits due to female choice. Female selection for bright colors and elaborate bowers provides the key to understanding the extraordinary number of cichlid species. Sexual selection is an accelerator of speciation. Slight variations in female preferences among males of different populations can lead to complete reproductive isolation. Females of one species of rock-dwelling cichlids prefer blue males, whereas females of sibling species prefer males with red fins. Females of a drab sand-dwelling species prefer males with the largest sand castle, while others prefer males with a complex array of multiple castles." -- McKaye
"Owing to his adoption of sympatric speciation, however, Darwin never needed to consider the geographical component in his theorizing."
"Unfortunately, by the time Darwin published the Origin (1859), he had adopted sympatric speciation (Mayr, 1982a). When he said that a new species might originate as a local variety, he did not necessarily mean an isolated population." -- Mayr (1992)
(5) From Change of the genetic environment
"We come thus to the important conclusion that the mere change of the genetic environment may change the selective value of a gene very considerably. Isolating a few individuals (the "founders") from a variable population which is situated in the midst of the stream of genes which flows ceaselessly through every widespread species will produce a sudden change of the genetic environment of most loci. This change, in fact, is the most drastic genetic change (except for polyploidy and hybridization) which may occur in a natural population, since it may affect all loci at once. Indeed, it may have the character of a veritable "genetic revolution." Furthermore, this "genetic revolution," released by the isolation of the founder population, may well have the character of a chain reaction. Changes in any locus will in turn affect the selective values at many other loci, until finally the system has reached a new state of equilibrium." -- Mayr (1954)
"Curiously, there is no chapter on speciation in Dobzhansky's book [Genetics and the Origin of Species]. His description of the isolating mechanisms was erroneous. Isolating mechanisms are genetic properties of individuals, yet he included geographic barriers among them. In addition, his putative species definition refers to the stage of a process, but is not the description of a (species) population. I was able to correct this in my 1942 book." -- Mayr (2004)