Hyperbolic theories of dissipation:: Why and when do we need them?

We illustrate and emphasize the relevance of hyperbolic theories of dissipation in different physical scenarios. Particular attention is paid to self-gravitating systems, where the relaxation time may become large enough as to require a description of the transient regime. It is argued that even outside that regime, hyperbolic theories may be needed to provide an accurate description of dissipative processes. (C) 2002 Elsevier Science B.V. All rights reserved.