I will give an overview of recent work on the statistical physics of lattice models of close-packed loops and their relation to quantum magnets. These models describe a number of problems in classical statistical physics -- where, for example, the loops may be vortex lines in a three-dimensional random field -- and also in antiferromagnets -- where the loops are world-lines of quantum particles. The loop models have two phases -- one in which all loops are finite, and another in which some loops are extended -- corresponding ground states of an antiferromagnet with respectively valence bond and Néel order. I will discuss the continuum description of these systems and present results from Monte Carlo simulations. In particular, these loop models are a convenient way to access the transition from the valence bond solid to a Neel states, which is a candidate deconfined critical point.