Chaos is not restricted to systems without any spatial extension: it in fact occurs commonly in spatially extended dynamical systems that are most typically described by nonlinear partial differential equations (PDEs). If the patterns generated by such a system change randomly in time, we speak of spatiotemporal chaos, a kind of temporally chaotic pattern-forming process. If, in addition, the patterns are also spatially irregular, there is fully developed spatiotemporal chaos. In principle, the phase-space dimension of a spatially extended dynamical system is infinite. However, in practice, when a spatial discretization scheme is used to solve the PDE, or when measurements are made in a physical experiment with finite spatial resolution, the effective dimension of the phase space is not infinite but still high.