The objectives in the application of targeted alpha therapy (TAT) for cancer therapy are reviewed. These relate to elimination of isolated cancer cells, cell clusters and tumors. Requirements for isolated cancer cells are good cellular targeting, high specific activity, and very short range. The regression of cell clusters in the peri-vascular space requires high capillary permeability and short range cross fire whereas for developed tumors, good bioavailabilty and anti- capillary activity are essential. Current sources of alpha radiation are reviewed and the prospects for commercial sources for clinical application are discussed. The Ac:Bi generator is the most practical alpha source, bringing therapy to Nuclear Medicine with the same practicality as the Mo:Tc generator has for imaging. The status quo of TAT is briefly reviewed with respect to dose normalization, real time microdosimetry and biological dosimetry for deterministic and stochastic effects and toxicity. The role of Monte Carlo calculations is emphasized. The strengths and weaknesses of TAT are examined and the way forward for clinical acceptance is discussed.