I'm in a comp bio PhD studying epigenetics in development and disease. Epigenetics can be thought of as the set of biochemical mechanisms other than the linear sequence of DNA that store and respond to information to control cell behavior. This is how normal development from a single zygote to an adult organism is controlled, why cells vary so much despite having (mutations/mosaicism aside) the same DNA, how cells respond to changing biochemical conditions, and where cancer comes from.

The classic example of epigenetics - of stable information transfer between cell generations not based on DNA sequence - is methylation of cytosines. Here's the simplified version. As you know, the DNA is based on ACTG. When you have a CG, the C can be methylated, which means an extra carbon is attached at a specific position on the molecule. That extra carbon gets 'copied' when the DNA is duplicated during mitosis and gets passed to the daughter cells. Yet it can be added or erased during the cell's lifetime. It typically works to block proteins responsible for transcribing genes into mRNA from binding to the gene, so the gene is silenced when it is methylated. This gives a way to transmit patterns of gene expression across generations of cells.

This mark is extremely well-studied and understanding everything about DNA methylation is beyond this humble PhD student. But there are also extremely mechanisms for erasing and/or resetting certain aspects of cell state during mitosis or meiosis, including RNA, the proteome, and methylation state. We can't take it for granted that just because there's a mechanism by which biochemical information could be transmitted that it actually is (or that it isn't).

A common source for the idea of intergenerational trauma being supported by epigenetic evidence is the Dutch hunger winter [1]. The idea is that an experience that parents had in utero seems to have had an effect on the physical development of their children, in a way that's specific to parental sex. I'm willing to say "sure, that effect could be real and there could be an epigenetic explanation." But AFAIK we don't know specifically what that hypothetical mechanism would have been.

Note that the bod(y|ies) of the mother and child are interchanging material and engaging in biochemical crosstalk constantly during gestation, so there is abundant opportunity for environmental influences on the mother to have lifelong impacts on the child. Since the child's body will in turn engage in the same 'dialog' with the child's own children during fertilization and gestation, it's entirely possible for environmental influences on generation 1 to impact generation 3 as mediated by generation 2 via an in utero exposure.

All that said, I have a lot of uncertainty about what our priors ought to be on how important such hypothetical mechanisms might be. I think that in the coming decades, we'll make huge progress in understanding development and disease within an individual's body through an epigenetic lens. We will probably also see some interesting controlled experiments on "epigenetic inheritance" using short-lived model organisms, such as fruit flies or worms. Possibly we will collect enough epigenetic information in large-scale biobanks over 20-40 years that we can get a more detailed understanding of possible epigenetic inheritance mechanisms in humans, but these assays are currently quite expensive, and moreover there's no single measure applicable to an individual person, since the whole point of epigenetics is that the state varies across cell and tissue type.

[1] https://www.ohsu.edu/school-of-medicine/moore-institute/dutc...