The past two decades have witnessed a surge in the use of numerical methods for the solution of problems from systems and control. This is due to a number of factors: the exploding growth in computer power; recent breakthroughs in optimization theory and algorithms, especially convex optimization; and recent advances in numerical linear algebra. As a result, a much wider class of problems in systems and control for which "analytical" solutions do not exist can now be efficiently solved using numerical methods. In this talk, we will focus on the application of convex optimization towards the solution of problems from systems and control, as well as from related areas such as communications, signal processing and robotics.