  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.
