Sequential quadratic programming (SQP) methods a powerful and effective class of methods for a wide range of nonlinearly constrained optimization problems. Given the scope and utility of nonlinear optimization, it is not surprising that SQP methods are still a subject of active research. Recent developments in methods for mixed integer nonlinear programming and the minimization of functions subject to differential equation constraints has led to a heightened interest in methods that may be "hot started" from a good approximate solution. We discuss the role of SQP methods in this context, with particular reference to some recent enhancements to our large-scale SQP package SNOPT. We end with some discussion of the challenges associated with formulating algorithms that can exploit multicore and GPU-based computer architectures.