Partial Differential Equations (PDEs) are ubiquitous in the sciences and engineering. Although very successful, traditional numerical methods can be very expensive, even infeasible, for a variety of problems. In this context, we present machine learning techniques that can accelerate and enable efficient computations of PDEs. We consider supervised deep learning, unsupervised learning in the form of physics informed neural networks (PINNs) and operator learning and describe how these frameworks are used to approximate PDEs. Both theoretical results as well as extensive numerical experiments will be presented.