The ability of climate models to simulate 20th century global mean sea level (GMSL) and regional sea-level change has been demonstrated. However, the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5) and Special Report on the Ocean and Cryosphere in a Changing Climate (SROCC) sea-level projections have not been rigorously evaluated with observed GMSL and coastal sea level from a global network of tide gauges as the short overlapping period (2007-2018) and natural variability make the detection of trends and accelerations challenging. Here, we critically evaluate these projections with satellite and tide-gauge observations. The observed trends from GMSL and the regional weighted mean at tide-gauge stations confirm the projections under three Representative Concentration Pathway (RCP) scenarios within 90% confidence level during 2007-2018. The central values of the observed GMSL (1993-2018) and regional weighted mean (1970-2018) accelerations are larger than projections for RCP2.6 and lie between (or even above) those for RCP4.5 and RCP8.5 over 2007-2032, but are not yet statistically different from any scenario. While the confirmation of the projection trends gives us confidence in current understanding of near future sea-level change, it leaves open questions concerning late 21st century non-linear accelerations from ice-sheet contributions.