This paper provides a survey on recent results on NMPC without terminal constraints. We investigate stability, performance and feasibility issues, both for classical stabilizing NMPC and for economic NMPC. Besides explaning and comparing different approaches obtained during the last couple of years, the paper also contains previously unpublished results and proofs for exponential convergence of economic NMPC performance and for recursive feasibility of stabilizing NMPC without stabilizing terminal constraints. Several examples are presented to illustrate our findings.