Numerous theoretical models suggest that sympatric speciation is possible when frequency-dependent interactions such as intraspecific competition drive disruptive selection on a trait that is also subject to assortative mating. Here, I review recent evidence that both conditions are met in lake populations of threespine stickleback (Gasterosteus aculeatus). Nonetheless, sympatric speciation appears to be rare or absent in stickleback. If stickleback qualitatively fit the theoretical requirements for sympatric speciation, why do they not undergo sympatric speciation? I present simulations showing that disruptive selection and assortative mating in stickleback, though present, are too weak to drive speciation. Furthermore, I summarize empirical evidence that disruptive selection in stickleback drives other forms of evolutionary diversification (plasticity, increased trait variance, and sexual dimorphism) instead of speciation. In conclusion, core assumptions of sympatric speciation theory seem to be qualitatively reasonable for stickleback, but speciation may nevertheless fail because of (i) quantitative mismatches with theory and (ii) alternative evolutionary outcomes.