As we are entering the era of precision cosmology, and the theory of primary cosmic microwave background (CMB) anisotropy is well-understood, new opportunities and challenges arise at the interface of theory and observation. In this talk I will focus on the issue of interpreting data from present and future CMB experiments. Present algorithms would take hundreds to millions of years of processor time to extract the angular power spectrum from forthcoming CMB data sets. We ask if a theoreticians toolbox can be usefully applied to these problems and find new methods which promise millionfold speed-ups over existing methods when applied to realistic data sets such as TOPHAT, MAP and Planck. If time permits I will briefly mention work on two other CMB frontiers, namely secondary anisotropies and polarization.