Some recent advances in nonlinear programming concepts and methods for nonlinear model predictive control are described and surveyed. These areas include the importance of : tailoring the nonlinear programming (NLP) algorithm to nonlinear model predictive control; a reliable NLP formulation to deal with open loop unstable control systems; efficient, large-scale algorithms for quadratic programming (QP) and NLP for on-line application of model predictive control (MPC); constraint handling for large-scale problems using interior point formulations. These concepts are illustrated by numerous examples. Open questions and future research directions are also discussed. In particular, the need to handle nominal and robust stability motivates more innovative NLP formulations and more powerful algorithms. The final section briefly mentions applications of NLP sensitivity analysis and nonconvex optimization to address these questions.