Naturally occurring tropical Pacific variations at timescales of 7–70 years — tropical Pacific decadal variability (TPDV) — describe basin-scale sea surface temperature (SST), sea-level pressure and heat content anomalies. Several mechanisms are proposed to explain TPDV, which can originate through oceanic processes, atmospheric processes or as an El Niño/Southern Oscillation (ENSO) residual. In this Review, we synthesize knowledge of these mechanisms, their characteristics and contribution to TPDV. Oceanic processes include off-equatorial Rossby waves, which mediate oceanic adjustment and contribute to variations in equatorial thermocline depth and SST; variations in the strength of the shallow upper-ocean overturning circulation, which exhibit a large anti-correlation with equatorial Pacific SST at interannual and decadal timescales; and the propagation of salinity-compensated temperature (spiciness) anomalies from the subtropics to the equatorial thermocline. Atmospheric processes include midlatitude internal variability leading to tropical and subtropical wind anomalies, which result in equatorial SST anomalies and feedbacks that enhance persistence; and atmospheric teleconnections from Atlantic and Indian Ocean SST variability, which induce winds conducive to decadal anomalies of the opposite sign in the Pacific. Although uncertain, the tropical adjustment through Rossby wave activity is likely a dominant mechanism. A deeper understanding of the origin and spectral characteristics of TPDV-related winds is a key priority.