This lecture describes recent work in our group on gapless mean-field theories for trapped Bose-Einstein condensates. We discuss the physical basis for these theories and compare them to the better known approaches. The proposed theories are based on suitable inclusion of the anomalous average of the Bose field operator. This leads to an effective interaction between two atoms which is both temperature and density dependent, as opposed to the widely used HFB-Popov approach for which it is constant. The predictions of these theories differ from the corresponding HFB-Popov ones by at most a few per cent for the lower-temperature gases studied in the laboratory at present. For systems that may well be studied in the next few years the effects can be much more profound. ©1999 American Institute of Physics.