The recently published Bedmap2 datasets mark the culmination of several decades of subice and subocean Antarctic topographic surveying by many nations, but maps of the topographic data distribution show that in the global context, the Antarctic bed remains very poorly sampled. Most of the remaining large unmapped areas on Earth lie under Antarctic ice and polar surveying continues to be difficult and expensive, thus it is important to identify where future efforts should be concentrated. A survey of 75 experts in various aspects of polar science shows that a lack of adequate topographic data is an important constraint in several themes, but the data gaps and the data needs do not tend to coincide. There is strong demand for higher resolution surveying in previously visited areas, particularly in the most dynamic and most rapidly changing regions as identified by glaciologists, oceanographers, hydrologists, biologists and geomorphologists, while geologists and ice core scientists focus on the most important areas for understanding Antarctica over deeper time. The data requirements identified here could be addressed for most areas given sufficient time and funding, but the technology needed to survey the interiors of the large ice shelf cavities has only just been developed.