Biomechanical modelling has the potential to start the next revolution in medicine, just as imaging has done in decades past. Current technology can now capture extremely detailed information about the structure of the human body. The next step is to consider function. Unfortunately, though there have been recent advances in creating useful anatomical models, there are still significant barriers preventing their widespread use. In this work, we aim to address some of the major challenges in biomechanical model construction. We examine issues of discretization: methods for representing complex soft tissue structures; issues related to consolidation of data: how to register information from multiple sources, particularly when some aspects are unreliable; and issues of detail: how to incorporate information necessary for reproducing function while balancing computational efficiency. To tackle discretization, we develop a novel hex-dominant meshing approach that allows for quality control. Our pattern-base tetrahedral recombination algorithm is extremely simple, and has tight computational bounds. We also compare a set of non-traditional alternatives in the context of muscle simulation to determine when each might be appropriate for a given application. For the fusion of data, we introduce a dynamics-driven registration technique which is robust to noise and unreliable information. It allows us to encode both physical and statistical priors, which we show can reduce error compared to the existing methods. We apply this to image registration for prostate interventions, where only parts of the anatomy are visible in images, as well as in creating a subject-specific model of the arm, where we need to adjust for both changes in shape and in pose. Finally, we examine the importance of and methods to include architectural details in a model, such as muscle fibre distribution, the stiffness of thin tendinous structures, and missing surface information. We examine the simulation of muscle contractions in the forearm, force transmission in the masseter, and dynamic motion in the upper airway to support swallowing and speech simulations. By overcoming some of these obstacles in biomechanical modelling, we hope to make it more accessible and practical for both research and clinical use.