Quantifying global trends and variability in sea surface temperature (SST) is of fundamental importance to understanding changes in the Earth’s climate. One approach to observing SST is via remote sensing. Here we use a 37-year gap-filled, daily-mean analysis of satellite SSTs to quantify SST trends, variability and persistence between 1981–2018. The global mean warming trend is 0.09 K per decade globally, with 95% of local trends being between −0.1 K and + 0.35 K. Excluding perennial sea-ice regions, the mean warming trend is 0.11 K per decade. After removing the long-term trend we calculate the SST power spectra over different time periods. The maximum variance in the SST power spectra in the equatorial Pacific is 1.9 K2 on 1–5 year timescales, dominated by ENSO processes. In western boundary currents characterised by an intense mesoscale activity, SST power on sub-annual timescales dominates, with a maximum variance of 4.9 K2. Persistence timescales tend to be shorter in the summer hemisphere due to the shallower mixed layer. The median short-term persistence length is 11–14 days, found over 71–79% of the global ocean area, with seasonal variations. The mean global correlation between monthly SST anomalies with a three-month time-lag is 0.35, with statistically significant correlations over 54.0% of the global oceans, and notably in the northern and equatorial Pacific, and the sub-polar gyre south of Greenland. At six months, the mean global SST anomaly correlation falls to 0.18. The satellite data record enables the detailed characterisation of temporal changes in SST over almost four decades.