In this talk I will present recent research results in scientific computing as applied toward biomedical computing and imaging. I will also discuss a sampling of these results within the context of an interactive problem-solving environment (BioPSE) for biomedical applications. As opposed to the typical "off-line" simulation mode - in which the scientist manually sets input parameters, computes results, visualizes the results via a separate visualization package, then starts again at the beginning - BioPSE "closes the loop" and allows interactive steering of the design, computation, and visualization phases of the simulation. I will also briefly discuss the advantages to using component architectures for this type of software and I will provide examples of several driving applications of steering and interactive visualization in cardiology (defibrillation simulation and device design), neuroscience (new inverse source localization techniques and surgical planning), and biomedical imaging (new methods for interactive processing and visualization of large-scale 3D MRI and CT volumes, and introduce new methods for diffusion tensor imaging).