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.