  Numerical simulations show that a massive real scalar field in a nonlinear
theory can form long-lived oscillating localized states. For a self-interacting
scalar on a fixed background these objects are named oscillons, while for the
self-gravitating case they are called oscillatons. This extensive review is
about the history and various general properties of these solutions, though
mainly focusing on the small but nonzero classical scalar field radiation
emitted by them. The radiation for higher amplitude states can be calculated by
a spectral numerical method. For small and moderately large amplitudes an
analytical approach based on complex extension, asymptotic matching and Borel
summation can be used. This procedure for the calculation of the energy loss
rate is explained in a detailed way in this review, starting with the simplest
one-dimensional scalar oscillons at first, and reaching to $3+1$ dimensional
self-gravitating oscillatons based on that experience.
