Detection of cardiac activation and reentry is critical in the diagnosis and treatment of arrhythmia, a heart disorder which affects some 4 million people in the US. Present approaches typically map the sequence of activation by using multiple catheters, or in particularly severe cases, by applying electrode arrays directly to the heart. Catheter based approaches usually measure signals from inside the heart chambers and thus detect only (sub)endocardial excitation and recovery. As a result, a substantial portion of ventricular tachycardias, those that have important epicardial components, cannot be fully characterized. Recent progress in the fabrication of multielectrode venous catheters permits simultaneous measurement from several catheters, each of which can have up to 16 individual electrodes, providing direct access to even distal segments of epicardial cardiac veins. While coverage of the epicardium is limited to the regions near these veins, we have shown that it is possible to estimate complete epicardial activation patterns from catheter based measurements, provided appropriate training data are available. In this paper we report on further testing of this direct estimation method. Beyond direct measurement and estimation, another possible approach to estimate epicardial activity is to solve the associated inverse problem in terms of epicardial potentials, which requires knowledge of the torso geometry and a numerical solution to Laplace’s equation. The challenges of this problem are formidable because of its ill-posed nature and the very high sensitivity of the solution to even small errors in boundary conditions or geometrical and electrical models. As a consequence, despite some notable recent results, solutions to this problem have not yet achieved clinical utility. The information available from catheter measurements made in the cardiac veins could be useful to improve the accuracy and robustness of such solutions. Thus, the overall goal of this research is to develop approaches that use the sparsely sampled information from these catheters both directly and as part of inverse solutions in order to develop more accurate epicardial mapping techniques without the need for open chest surgery and direct access to the heart. Here we describe recent results in catheter lead selection for the estimation approach and also a novel means of using catheter signals to improve the accuracy of epicardial inverse solutions.