Sea-level change is one of the major consequences of climate change and is projected to affect coastal communities around the world. Here, we compare Global Mean Sea-Level (GMSL) change estimated by 12 climate models from the 5th phase of the World Climate Research Programme’s Climate Model Intercomparison Project (CMIP5) to observational estimates for the period 1900-2015. We analyse observed and simulated individual contributions to GMSL change (thermal expansion, glacier mass change, ice sheet mass change, landwater storage change) and compare the summed simulated contributions to observed GMSL change over the period 1900-2007 using tide gauge reconstructions, and over the period 1993-2015 using satellite altimetry estimates. The model-simulated contributions allow us to explain 50 ± 30% (uncertainties 1.65σ unless indicated otherwise) of the mean observed change from 1901-1920 to 1988-2007. Based on attributable biases between observations and models, we propose to add a number of corrections, which result in an improved explanation of 75 ± 38% of the observed change. For the satellite era (1993-1997 to 2011-2015) we find an improved budget closure of 102 ± 33% (105 ± 35% when including the proposed bias corrections). Simulated decadal trends over the 20th century increase, both in the thermal expansion and the combined mass contributions (glaciers, ice sheets and landwater storage). The mass components explain the majority of sea-level rise over the 20th century, but the thermal expansion has increasingly contributed to sea-level rise, starting from 1910 onwards and in 2015 accounting for 46% of the total simulated sea-level change.