  We discuss effects of various impurities on the magnetic susceptibility and
the specific heat of the quantum S=1/2 Heisenberg antiferromagnet on a
two-dimensional square lattice. For impurities with spin S_i > 0 (here S_i=1/2
in the case of a vacancy or an added spin, and S_i=1 for a spin coupled
ferromagnetically to its neighbors), our quantum Monte Carlo simulations
confirm a classical-like Curie susceptibility contribution S_i^2/4T, which
originates from an alignment of the impurity spin with the local N\'eel order.
In addition, we find a logarithmically divergent contribution, which we
attribute to fluctuations transverse to the local N\'eel vector. We also study
frustrated and nonfrustrated bond impurities with S_i=0. For a simple intuitive
picture of the impurity problem, we discuss an effective few-spin model that
can distinguish between the different impurities and reproduces the
leading-order simulation data over a wide temperature range.
