We study the field dependence of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice by means of exact diagonalizations. In the first part, we calculate the spin-wave velocity c, the spin stiffness rho(s), and the magnetic susceptibility chi(perpendicular to), and thus determine the microscopic parameters of the low-energy long-wavelength description. In the second part, we present a comprehensive study of dynamical spin-correlation functions for magnetic fields ranging from zero up to saturation. We find that, at low fields, magnons are well defined in the whole Brillouin zone but the dispersion is substantially modified by quantum fluctuations compared to the classical spectrum. At higher fields, decay channels open and magnons become unstable with respect to multimagnon scattering. Our results directly apply to inelastic neutron-scattering experiments.