So far, we have discussed discrete interface models. Taking their (mesoscopic) continuum limit, as a time evolution of interfaces or some other related physical order parameters, one would expect to obtain stochastic partial differential equations (SPDEs), which are partial differential equations having stochastic terms such as a space-time Gaussian white noise. In connection with the problem of random interfaces, we will especially discuss a stochastic Allen-Cahn equation, sometimes called the time-dependent Ginzburg-Landau (TDGL) equation or a dynamic P(ϕ)-model, in Chap. 4, and the Kardar-Parisi-Zhang (KPZ) equation in Chap. 5 This chapter explains, taking the TDGL equation as an example, some fundamental facts concerning SPDEs such as white noises, colored noises, definitions and regularities of solutions of the SPDEs we are interested in. We give some other examples of related SPDEs. The SPDEs used in physics are sometimes ill-posed. They appear in a wide variety of fields, not only in physics but also in biology, engineering (e.g., in control theory, filtering), economics (e.g., in mathematical finance), and others.