Adaptive processing and classification of electrocardiogram (ECG) signals are important in eliminating the strenuous process of manually annotating ECG recordings for clinical use. Such algorithms require robust models whose parameters can adequately describe the ECG signals. Although different dynamic statistical models describing ECG signals currently exist, they depend considerably on a priori information and user-specified model parameters. Also, ECG beat morphologies, which vary greatly across patients and disease states, cannot be uniquely characterized by a single model. In this work, sequential Bayesian based methods are used to appropriately model and adaptively select the corresponding model parameters of ECG signals. An adaptive framework based on a sequential Bayesian tracking method is proposed to adaptively select the cardiac parameters that minimize the estimation error, thus precluding the need for pre-processing. Simulations using real ECG data from the online Physionet database demonstrate the improvement in performance of the proposed algorithm in accurately estimating critical heart disease parameters. In addition, two new approaches to ECG modeling are presented using the interacting multiple model and the sequential Markov chain Monte Carlo technique with adaptive model selection. Both these methods can adaptively choose between different models for various ECG beat morphologies without requiring prior ECG information, as demonstrated by using real ECG signals. A supervised Bayesian maximum-likelihood (ML) based classifier uses the estimated model parameters to classify different types of cardiac arrhythmias. However, the non-availability of sufficient amounts of representative training data and the large inter-patient variability pose a challenge to the existing supervised learning algorithms, resulting in a poor classification performance. In addition, recently developed unsupervised learning methods require a priori knowledge on the number of diseases to cluster the ECG data, which often evolves over time. In order to address these issues, an adaptive learning ECG classification method that uses Dirichlet process Gaussian mixture models is proposed. This approach does not place any restriction on the number of disease classes, nor does it require any training data. This algorithm is adapted to be patient-specific by labeling or identifying the generated mixtures using the Bayesian ML method, assuming the availability of labeled training data.