Nonadiabatic events, in which the Born-Oppenheimer approximation breaks down, are ubiquitous in chemistry and biology. It is now widely accepted that they are facilitated by conical intersections (CIs), actual degeneracies between electronic states. We review the basic theory of CIs and how they can be studied using modern quantum chemistry and nuclear dynamics. We highlight their importance by presenting their role in radiationless decay pathways present in the building blocks of DNA and proteins. The presence of CIs may contribute to the photostability of these important biomolecules.