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Cardiovascular diseases, including heart diseases and stroke, are the leading cause of death all over the world. Researchers have been extensively working on methods for early diagnosis and treatment of these diseases, with the goal of decreasing these death tolls. One of the cutting edge research topics on heart diseases is the noninvasive electrocardiographic imaging (ECGI), in which the electrical activity of the heart is estimated from electrocardiographic measurements obtained from the body surface, using densely distributed electrodes, and a mathematical model of the body. From a mathematical point of view, this estimation problem is called the “inverse problem of electrocardiography (ECG).” Since this technique provides high resolution images of the electrical activity directly on the heart surface without actually placing electrodes on the heart, it is a superior alternative to classical ECG, which is the most widely used technique in clinics to obtain information on heart pathologies. In the classical ECG, only a limited number of electrodes can be placed on the body surface, and the electrical activity is obtained indirectly, which causes loss of information. In this talk, I will present past and present research on ECGI in the Heart Research Laboratory. We mainly focus on solving the inverse ECG problem using statistical estimation techniques such as Bayesian Estimation and Kalman Filtering. These techniques are advantageous over traditional methods due to their flexibility in incorporating the spatial and temporal information of the heart potentials for solving the inverse ECG problem, and yielding confidence intervals that help assess the accuracy of the solutions.