Ongoing observations of the Cosmic Microwave Background, such as the MAXIMA and BOOMERanG projects, are providing datasets of unprecedented quality and ever-increasing size. Exact analysis of the data they produce is a serious computational challenge, currently scaling as the number of sky pixels squared in memory and cubed in time. Here we discuss the origins of these scaling relations and their implications for our efforts to extract precise cosmological parameters from observations of the CMB. ©1999 American Institute of Physics.