In this talk we discuss the well-posedness of nonlinear wave equations with rough and random initial data. Even if the initial data lives at a regularity for which deterministic ill-posedness is known, we show that one can still construct solutions in an almost sure sense. In the beginning of the talk we will review the basic deterministic theory for nonlinear wave equations. Then, we will describe the construction of the randomized initial data. The focus in this talk lies on a randomization that yields spherically symmetric initial data. This leads to an interesting trade-off between geometric structure (spherical symmetry) and randomness. Finally, we will discuss the global behaviour of solutions to the radial energycritical nonlinear wave equation with random initial data. To this end, we introduce a novel interaction flux estimate.