Using lattice QCD, one can study hadrons and their interactions starting from quantum chromodynamics. In the baryon-baryon sector, this offers the prospect of a first-principles basis for nuclear physics. I will discuss the methodology and challenges of these calculations and present a study of the conjectured H dibaryon, a bound state of hyperons with quark content uuddss, at a single SU(3)-flavour-symmetric quark mass point. For the first time, an extrapolation to zero lattice spacing was performed, which had an unexpectedly large effect on the binding energy. Concerning nucleon-nucleon interactions, I will review the status of past calculations and present some work in progress.