  External fluctuations have a wide variety of constructive effects on the
dynamical behavior of spatially extended systems, as described by stochastic
partial differential equations. A set of paradigmatic situations exhibiting
such effects are briefly reviewed in this paper, in an attempt to provide a
concise but thorough introduction to this active field of research, and at the
same time an overview of its current status. This work is dedicated to Lutz
Schimansky-Geier on the occassion of his 50th anniversary. Through the years,
Prof. Schimansky-Geier has made important contributions to the field of
spatiotemporal stochastic dynamics, including seminal investigations in the
early 1990's on noise effects in front propagation, and studies of
noise-induced phase transitions and noise-sustained structures in excitable
media, among others.
