The answer is, of course, not much. A subject near and dear to my heart: Evolution, Entropy, and Information, over at Cosmic Variance, referencing John Baez’s great series on information geometry (latest entry here).
For a project I’m working on, I’ve lately been considering the various ways your DNA can be considered to contain information, and how we can use information content to read DNA sequences. Information theory has of course been used for a long time to find functional sequences in DNA (see this classic paper). This is what we call bioinformatics, but there are also more physical reasons to use information theory to understand biology. There are deep relationships between information, thermodynamics, and computation (PDF), which we can use to understand how the thermodynamic system of the cell processes information contained within DNA.
There will be more on this in the future, but in the mean time, go check out the links.