We present  recent advancements in the field of asynchronous parallel methods for the minimization of the sum of a differentiable function and a possibly nonsmooth, convex regularizer subject to constraints. In recent years, problems of this kind have played an important role in many applicative fields, e.g. in machine learning,  data mining, and compressed sensing, and instances of ever increasing dimensions need to be solved. Asynchronous methods play a key role in the solution of these large problems. After reviewing recent results in the field, we discuss, in particular, a rather general framework  along with its main convergence properties  and  report numerical results.