When alleles have pleiotropic effects on a number of quantitative traits, the degree of dominance between a pair of alleles can be different for each trait. Such trait-specific dominance has been studied previously in models for the maintenance of genetic variation by antagonistic effects of an allele on two fitness components. By generalizing these models to an arbitrary number of fitness components or other phenotypic traits with different degrees of dominance, I show that genetic polymorphism is generally impossible without antagonistic fitness effects of different traits and without trait-specific dominance. I also investigate dominance and pleiotropy from a more long-term evolutionary perspective, allowing for the study of general ecological scenarios, and I discuss the effects of trait-specific dominance on evolutionary stability criteria. When selection is mainly directional and only trait-specific dominance and antagonism cause the emergence of polymorphism, then these polymorphisms can be overtaken by single mutants again, such that they are probably short-lived on an evolutionary time scale. Near evolutionarily singular points where directional selection is absent, trait-specific dominance and overdominance facilitate the emergence of polymorphism and cause evolutionary divergence in some cases. An important outcome of these models is that trait-specific dominance allows for the emergence of genetic polymorphisms without a selective disadvantage for heterozygotes. This removes the scope for the evolution of assortative mate choice and affects dominance modification. Sympatric speciation by disruptive ecological selection requires this heterozygote disadvantage in order to evolve, and therefore it becomes less plausible if the emergence of genetic polymorphism usually occurs via trait-specific dominance and antagonistic effects.