From Wikipedia:
“Lamarckism (or Lamarckian inheritance) is the idea that an organism can pass on characteristics that it acquired during its lifetime to its offspring (also known as heritability of acquired characteristics or soft inheritance).”

But Charles Darwin and Gregor Mendel disproved this, right? (And we’ll let slide the fact that it is now fairly accepted that Mendel fudged his famous results when they didn’t quite match up to his early understanding of genetics.)

Well, yes. And as so often happens in the pursuit of science, now the tables are getting cocked sideways with the rise of epigenetics and the very real evidence the while genes are inherited, their expression may indeed be acquired by the previous generation’s experiences

As noted in Discover:

Your ancestors’ lousy childhoods or excellent adventures might change your personality, bequeathing anxiety or resilience by altering the epigenetic expressions of genes in the brain.

Since the 1970s, researchers had known that the tightly wound spools of DNA inside each cell’s nucleus require something extra to tell them exactly which genes to transcribe, whether for a heart cell, a liver cell or a brain cell.

Originally these epigenetic changes were believed to occur only during fetal development. But pioneering studies showed that molecular bric-a-brac could be added to DNA in adulthood, setting off a cascade of cellular changes resulting in cancer.

Now, of course, the field of epigenetics is thriving, and it is suddenly not merely plausible, but actually likely that through this mechanic what was once thought impossible – the passing of effects based on experiences of one generation to the next – is now very likely happening.

What kinds of effects are we talking about?

Details are still somewhat speculative, but at the very least it is thought now that severe stress in the parents may, for example, increase the chance of depression in their offspring.

Via Discover for the full article, and Wikipedia for more background on Lamarckism.