The heart is an essential heterogeneous organ that depends on strong coupling between electrical, chemical, and mechanical dynamics to properly function as a pump that supplies blood to the rest of the body. Cardiac arrhythmias are common disorders characterized by irregular beating of the heart that lead to serious clinical conditions. It is estimated that approximately 2.2 million adults in the United States are affected by atrial fibrillation, a prevalent arrhythmia. Unfortunately, a clinician often does not have enough information to diagnose a patient's heart condition to determine the optimal treatment procedure. This is an area that computational mechanics can address. While development of mechanical and electrophysiological models of cardiac tissue primarily started in the 1950s, fully-coupled models have only more recently been developed due to factors regarding computational cost, difficulty in quantifying material properties, and difficulty in integrating complex models in a cohesive and efficient manner. Therefore, in order for simulation tools to have impact in the clinical or experimental setting, these tools must be efficient, fast, robust, and accessible. The focus of this thesis is to develop methods of addressing the aforementioned issues and then illustrate how efficient electromechanical finite element models can be developed for the heart such that their use in the clinical and experimental setting can be realized in several examples. In this thesis, a global-local variable splitting formulation borrowed from the field of plasticity is used to address the issues of complex model integration, and to maintain numerical stability at low costs. Through careful examination of classical phenomenological models and detailed biophysical ionic models of the electrophysiology of the heart, almost all models can be reformulated into this global-local splitting framework. The numerical properties of cost-expensive ionic models are briefly analyzed within the context of this framework. Use of implicit-time stepping in tandem with a simple iteration and error tolerance based adaptive time-stepping algorithm allows for reduction of computation time from hours to minutes. Flexibility and modularity of the framework are illustrated through the development of electrical, electro-chemical, electro-chemical-mechanical, and opto-electro-mechanical models of cardiac tissue. The heart is modeled efficiently using custom finite element ventricular cell models for physiological electrical simulations and large deformation excitation-contraction dry-pumping simulations of the heart. The results accurately model the physiological condition of the heart. The flexibility and multiscale nature of the framework is also leveraged in developing novel optical-induced cardiac cell excitation models of new genetically engineered Channelrhodpsin-2 (ChR2) cardiac myocytes. An ionic model was developed for these particular bio-engineered stem cells, calibrated with experimental data from collaborators, and was able to predict the electrical excitation behavior of the cells to a reasonable degree of accuracy. This model was then combined with ionic pacemaker cell models and also with ventricular cell models into respective finite elements to simulate experiments and predict future therapies using ChR2 genetically modified cardiac tissue. The thesis also addresses difficulties relating to identification and characterization of material parameter identification in inhomogeneous cardiac tissue. Metrics for determining smoothness in electrical conduction in tissue cultures were validated with stochastic finite element models of microelectrode array cell conduction experiments. The results indicate that these metrics are useful in characterizing different conduction patterns based on two metrics borrowed from texture analysis. Difficulties in obtaining structural fiber data from clinical images were addressed by developing an algorithmic method for designating approximate physiologically accurate fiber distributions for the heart using only geometrical information obtained from MRI scans of the surfaces of the heart. Poisson interpolation is used and results in a smooth continuous rotating fiber description that matches experimentally obtained fiber directions from MRI scans. The main benefits of this algorithm are its simplicity of implementation, physiologically accuracy, and generality in interpolating fiber distributions. Lastly, the thesis demonstrates possible benefits of GPU computing in order to achieve near-real-time electrical simulations of arrhythmias in the heart. The assembly and solver routines from the finite element code, FEAP from Berkeley, were ported to the GPU using CUDA. Even with a minimally optimized proof-of-concept, the GPU-only finite element code achieves performance comparable to twelve cores using only one GPU. To increase the overall efficiency of the method, current sparse matrix vector multiplication GPU algorithms are analyzed, and possible alternative algorithms are developed specifically with unstructured finite element meshes in mind. Altogether, the different methods developed in this thesis have been shown to be effective in addressing issues related to efficiency, numerical stability, modularity, and flexibility in real computational applications of the heart. Special consideration was taken in designing the different methods to be compatible with one another, such that a majority of the methods could be integrated and the benefits of each method could be leveraged with each other to gain maximum efficiency. While these developed methods can still be improved, the thesis work as a whole serves to demonstrate and highlight future uses for computational models within experimental and clinical settings.