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The study of compressor instabilities in gas turbine engines has received much attention in recent years. In particular, rotating stall and surge are major causes of problems ranging from component stress and lifespan reduction to engine explosion. In this thesis, modeling and control of rotating stall and surge using bleed valve and air injection is studied and validated on a low speed, single stage, axial compressor at Caltech. <p> Bleed valve control of stall is achieved only when the compressor characteristic is actuated, due to the fast growth rate of the stall cell compared to the rate limit of the valve. Furthermore, experimental results show that the actuator rate requirement for stall control is reduced by a factor of fourteen via compressor characteristic actuation. Analytical expressions based on low order models (2--3 states) and a high fidelity simulation (37 states) tool are developed to estimate the minimum rate requirement of a bleed valve for control of stall. A comparison of the tools to experiments show a good qualitative agreement, with increasing quantitative accuracy as the complexity of the underlying model increases. <p> Air injection control of stall and surge is also investigated. Simultaneous control of stall and surge is achieved using axisymmetric air injection. Three cases with different injector back pressure are studied. Surge control via binary air injection is achieved in all three cases. Simultaneous stall and surge control is achieved for two of the cases, but is not achieved for the lowest authority case. This is consistent with previous results for control of stall with axisymmetric air injection without a plenum attached. <p> Non--axisymmetric air injection control of stall and surge is also studied. Three existing control algorithms found in literature are modeled and analyzed. A three--state model is obtained for each algorithm. For two cases, conditions for linear stability and bifurcation criticality on control of rotating stall are derived and expressed in terms of implementation--oriented variables such as number of injectors. For the third case, bifurcation criticality conditions are not obtained due to complexity, though linear stability property is derived. A theoretical comparison between the three algorithms is made, via the use of low--order models, to investigate pros and cons of the algorithms in the context of operability. <p> The effects of static distortion on the compressor facility at Caltech is characterized experimentally. Results consistent with literature are obtained. Simulations via a high fidelity model (34 states) are also performed and show good qualitative as well as quantitative agreement to experiments. A non--axisymmetric pulsed air injection controller for stall is shown to be robust to static distortion.