  This survey is devoted to the asymptotic behavior of solutions of evolution
equations generated by maximal monotone operators in Hilbert spaces. The
emphasis is in the comparison of the continuous time trajectories to sequences
generated by implicit or explicit discrete time schemes. The analysis covers
weak convergence for the average process, for the process itself and strong
convergence and aims at highlighting the main ideas and unifying the proofs. We
further make the connection with the analysis in terms of almost orbits that
allows for a broader scope.
