Surface mass balance (SMB) provides mass input to the surface of the Antarctic and Greenland Ice Sheets and therefore comprises an important control on ice sheet mass balance and resulting contribution to global sea level change. As ice sheet SMB varies highly across multiple scales of space (meters to hundreds of kilometers) and time (hourly to decadal), it is notoriously challenging to observe and represent in models. In addition, SMB consists of multiple components, all of which depend on complex interactions between the atmosphere and the snow/ice surface, large‐scale atmospheric circulation and ocean conditions, and ice sheet topography. In this review, we present the state‐of‐the‐art knowledge and recent advances in ice sheet SMB observations and models, highlight current shortcomings, and propose future directions. Novel observational methods allow mapping SMB across larger areas, longer time periods, and/or at very high (subdaily) temporal frequency. As a recent observational breakthrough, cosmic ray counters provide direct estimates of SMB, circumventing the need for accurate snow density observations upon which many other techniques rely. Regional atmospheric climate models have drastically improved their simulation of ice sheet SMB in the last decade, thanks to the inclusion or improved representation of essential processes (e.g., clouds, blowing snow, and snow albedo), and by enhancing horizontal resolution (5–30 km). Future modeling efforts are required in improving Earth system models to match regional atmospheric climate model performance in simulating ice sheet SMB, and in reinforcing the efforts in developing statistical and dynamic downscaling to represent smaller‐scale SMB processes.