Bluff body flows controlled in various manners are simulated with a high-resolution, gridless vortex method. Two-dimensional, unsteady, viscous simulations are utilized to illuminate the physical phenomenon underpinning certain flows of this class. Flows past a rotationally oscillating circular cylinder and flows past an elastically mounted circular cylinder are studied, providing a variety of new insights about these systems. A computational method facilitating longtime, high-resolution vortex simulations is developed whose grid-free nature enables future extension to complex geometries. The significant fluid forces experienced by bluff bodies are of much practical concern and are induced by flowfields that are often complex. The studies in this thesis aim to contribute to the understanding of the relation between wake development and forces and how to exploit this relationship to achieve flow control. A circular cylinder undergoing rotational oscillation is known to experience a significant deviation in forces from unforced flow. Computations from Re=150-15000 verify past experimental observation of significant drag reduction for certain forcing parameters. These simulations also illuminate the mechanism which renders this control effective - a forced boundary layer instability triggering premature shedding of multipole vortex structures. New insights were also provided by studies of flow over a model of an elastically mounted cylinder. A two-dimensional cylinder modeled as a damped oscillator can serve as an approximation to three-dimensional situations such as a cable under tension. Simulations clarified the behavior of such a two-dimensional system and, contrary to a line of classical thinking, revealed an unexpected adaptivity in wake evolution. New scaling is also suggested which better classifies these systems under certain conditions. Vortex methods are well-suited for incompressible bluff body flow in many ways. However, the handling of viscous diffusion causes complications for such simulations. A relatively unexplored approach, the core expansion method, is studied, extended, and implemented in this work in order to balance accuracy with preservation of the gridless foundation of vortex methods. This viscous technique is found to enable long-time calculations that are prohibitive with other techniques while preserving a high level of accuracy.