  We calculate the Raman spectrum of the two-dimensional (2D) spin-1/2
Heisenberg antiferromagnet by exact diagonalization and quantum Monte Carlo
techniques on clusters of up to 144 sites and, on a 16-site cluster, by
considering the phonon-magnon interaction which leads to random fluctuations of
the exchange integral. Results are in good agreement with experiments on
various high-T_c precursors, such as La_2CuO_4 and YBa_2Cu_3O_{6.2}. In
particular, our calculations reproduce the broad lineshape of the two-magnon
peak, the asymmetry about its maximum, the existence of spectral weight at high
energies, and the observation of nominally forbidden A_{1g} scattering.
