A brief review of our research work, at IIT Kanpur, during the past seven years is presented. Modern finite element methods have been utilized to compute fluid flows involving 3D, unsteady turbulent flows past bodies complex at various Reynolds and Mach numbers. The stabilized finite element methods that are being used are robust, accurate and able to handle complex geometries including those that deform with time. The research program has been tailored to cater to various sponsored and research projects of national interest .In addition, certain problems to increase fundamental understanding have been attempted.