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The East Antarctic Ice Sheet is the largest, highest, coldest, driest, and windiest ice sheet on Earth. Understanding of the surface mass balance (SMB) of Antarctica is necessary to determine the present state of the ice sheet, to make predictions of its potential contribution to sea level rise, and to determine its past history for paleoclimatic reconstructions. However, SMB values are poorly known because of logistic constraints in extreme polar environments, and they represent one of the biggest challenges of Antarctic science. Snow accumulation is the most important parameter for the SMB of ice sheets. SMB varies on a number of scales, from small-scale features (sastrugi) to ice-sheet-scale SMB patterns determined mainly by temperature, elevation, distance from the coast, and wind-driven processes. In situ measurements of SMB are performed at single points by stakes, ultrasonic sounders, snow pits, and firn and ice cores and laterally by continuous measurements using ground-penetrating radar. SMB for large regions can only be achieved practically by using remote sensing and/or numerical climate modeling. However, these techniques rely on ground truthing to improve the resolution and accuracy. The separation of spatial and temporal variations of SMB in transient regimes is necessary for accurate interpretation of ice core records. In this review we provide an overview of the various measurement techniques, related difficulties, and limitations of data interpretation; describe spatial characteristics of East Antarctic SMB and issues related to the spatial and temporal representativity of measurements; and provide recommendations on how to perform in situ measurements.