In their 1978 paper, Dyson, Lieb, and Simon (DLS) proved the existence of Ne'el
order at positive temperature for the spin-S Heisenberg antiferromagnet on the
d-dimensional hypercubic lattice when either S >= 1 and d >= 3 or S=1/2 and d is
sufficiently large. This was the first proof of spontaneous breaking of a continuous
symmetry in a quantum model at finite temperature. Since then the ideas of DLS have been
extended and adapted to a variety of other problems. In this paper I will present an
overview of the most important developments in the study of the Heisenberg model and
related quantum lattice systems since 1978, including but not restricted to those directly
related to the paper by DLS.