For a long time we thought we had a pretty good idea about how heredity works. At first it was just "offspring look roughly like a combination of their parents". Then Mendel figured out dominant and recessive traits, among other features of genetics. Between evolution and the discovery of DNA, our modern understanding of heredity seemed pretty solid. Especially in the case of sexual reproduction, a huge amount of information is transferred, combined, and stored. Unfortunately, it's not that simple, and again it wasn't very simple to begin with.
For the last few years and extremely hot topics has been epigenetics, which broadly speaking is the study of proteins and other molecules related to gene regulations. Basically, if DNA is like a language with only four letters, epigenetics is an extremely complex dewey decimal system. It's an entirely different set of systems that determines what parts of the DNA actually get read and how it's all organized.
Naturally, gene regulation is dynamic and responds to the environment. Factors like disease, diet, and drug use, can all affect how genes are expressed in different tissue types. Some scientists suspect that modification to these regulatory mechanisms could be passed on to the next generation, in addition to DNA itself. Other think that the epigenetic slate might be wiped clean, due to how different gene expression needs to be during embryonic development.
However, recent research from the University of Edinburgh may be supporting that first hypothesis. (via ScienceDaily) They looked at yeast with very similar gene regulation mechanisms to humans, and specifically looked at proteins called histones. DNA is extremely long, so fitting it inside a cell requires a lot of packaging. Histones are the first level of packaging that DNA wraps around. Since the DNA needs to be accessible to be transcribed into RNA, DNA packaging and gene regulation are tightly linked.
Histones are naturally modified in the course of an organism's lifecycle, but these researchers added a few of their own. They found that the modifications they made could be tracked over multiple generations, and that this affected how nearby genes are expressed.
This is a big boost for the idea that the decisions and environment of a parent can more complexly effect offspring. The idea is that any damage or other modification to certain gene regulation proteins could have adverse effects in the offspring. Some research has suggested such a mechanism in humans, but that cannot be fully confirmed through this research alone; more study is needed.