Contact line dynamics offers a challenging problem of computational fluid dynamics. Among the most difficult issues is the very wide range of scales involved, from orders of magnitude below the nanometer to the macroscopic scale in some cases. Attempts at investigating the contact line problem have been made from various approaches, the closest to first principles being molecular dynamics, while diffuse interface methods and sharp interface methods with several variants have also been put forward. The talk will review the corresponding efforts made on a number of problems, including plunging and withdrawing plates, the sheared droplet, sessile droplets on oscillating or accelerating substrates, menisci in nanopores and the hydrodynamics assist problem. The issues involved in nucleate boiling and accelerated sessile droplets will be addressed both from the point of view of experiments performed by various colleagues and from simulations.