The GPS and CSS sources have remained outside the mainstream paradigm for powerful radio sources since their discovery. Below I review the three main hypotheses for their nature. These ideas were all suggested to explain the facts that these sources are (1) compact, (2) very radio luminous (as powerful as the large 3CR classical doubles), and (3) a significant fraction of the radio source population. The simplest hypothesis, that the compact sources evolve with constant radio luminosity and constant advance speed into the large ones, fails because of their large relative numbers, i.e., if the GPS sources have lifetimes that are 10-3 of the large classical doubles, then they should also be 10-3 less numerous, yet they are at least 10% of the bright radio source population.
Readhead et al. (1994)
suggested that the CSOs might be transient events with relatively short
lifetimes of 
104 yr (see also
Readhead et al. 1996b).
Given the short lifetimes of the implied CSO phase, most elliptical
galaxies with luminosities of at least 0.3L*
or more would pass through a CSO phase at least once. Since we now know
that the host galaxies of the CSO (and in general GPS) galaxies are
L* or brighter, this decreases the possible
parent population of CSOs and increases the number of times each galaxy
must go through a CSO phase. In its current simple form, this hypothesis
lacks predictive power. At this point there are no strong arguments
either for or against it, other than Occam's razor.