Compact steep-spectrum (CSS) and peaked spectrum (PS) radio sources are compact, powerful radio sources. The multi-frequency observational properties and current theories are reviewed with emphasis on developments since the earlier review of ODea (1998). There are three main hypotheses for the nature of PS and CSS sources. (1) The PS sources might be very young radio galaxies which will evolve into CSS sources on their way to becoming large radio galaxies. (2) The PS and CSS sources might be compact because they are confined (and enhanced in radio power) by interaction with dense gas in their environments. (3) Alternately, the PS sources might be transient or intermittent sources. Each of these hypotheses may apply to individual objects. The relative number in each population will have significant implications for the radio galaxy paradigm. Proper motion studies over long time baselines have helped determine hotspot speeds for over three dozen sources and establish that these are young objects. Multifrequency polarization observations have demonstrated that many CSS/PS sources are embedded in a dense interstellar medium and vigorously interacting with it. The detection of emission line gas aligned with the radio source, and blue-shifted HI absorption and [OIII] emission lines indicates that AGN feedback is present in these objects -- possibly driven by the radio source. CSS/PS sources with evidence of episodic AGN over a large range of time-scales have been discussed. The review closes with a discussion of open questions and prospects for the future.
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