This is a good summary:
Since I started this website, I’ve written many posts on epigenetics, a term that now refers to modification of the nucleotide base composition of DNA by the environment or by other genes. Such modification—usually involving attachment of methyl groups to two of the four bases that make up DNA—may have significant effects on the organism, ranging from changed behavior to changed appearance. But “epigenetics” has been taken up by the “Darwin-was-wrong” crowd as a way to claim that environmentally induced epigenetic modifications of the DNA can be inherited in a stable fashion over generations and even produce adaptations—a decidedly non-Darwinian mode of evolution called “Lamarckian inheritance.”
You can read my previous posts, grouped under the link above, for my skeptical views on this alternative route to the evolution of adaptations. There’s no doubt that epigenetic modification of DNA can be produced by “instructions” from other parts of the DNA, and that those genetically-based modifications can be adaptive. They can, for instance, explain why the genes from mothers versus fathers act antagonistically in the fetus, as paternal DNA is “imprinted” (methylated) differently from maternal DNA, and fathers have different reproductive interests from mothers. But this sort of epigenetic modification ultimately rests on genetic adaptation: the “instructions” coded in parental genomes. It is not something induced purely by the environment.
As for purely environmental modification of DNA, that can on occasion affect the organism, but almost never persists beyond one or two generations (the methyl groups disappear during sperm and egg formation), and to my knowledge is not responsible for a single permanent adaptation seen in nature. When the genetic basis of adaptations like spiny fins, cryptic coloration in mice, or beak width in finches is studied, it invariably rests not on environmentally-aquired epigenetic modifications, but on base-pair changes in DNA—that is, on the conventional neo-Darwinian paradigm of “random” mutations in the DNA that change its sequence, with those changes enhancing reproduction being the ones that persist. In other words, virtually every adaptation ever studied is based on conventional mutations and natural selection, not environmentally induced changes of the DNA that persist for generation after generation. What persists are the claims of would-be Kuhnians who see epigenetics as a highly significant route to adaptive evolution—one that violates conventional wisdom.