We investigate the Polya process, which underlies an urn of white and blue balls growing in real time. A partial differential equation governs the evolution of the process. Some special cases are amenable to exact and asymptotic solution: they include the (forward or backward) diagonal processes, and the Ehrenfest process. Applications of standard (discrete) urns and their analogue when embedded in real time include several classes of random trees that have applications in computer science (design and analysis of algorithms), epidemiology and philology. We shall present some of these applications.