The recent advent of micro-electro-mechanical systems has increased the demand for localized energy harvesting. The autonomous gadgets, structural health monitoring sensors, wireless sensors, and pacemakers are all paving their ways in our lives. These electronic devices demand innovative ways of powering them effectively and efficiently. Various ambient excitations can be used from the environment like base or aeroelastic. For converting this wasted mechanical energy, several transduction mechanisms are employed, like piezoelectric, electromagnetic, and electrostatic. This dissertation is a step forward in meeting the localized energy demand for operating low-power electronic devices by using a hybrid formation of piezoelectric material and electromagnet-coil arrangement for harnessing aeroelastic oscillations. Therefore in the first part of this dissertation, this hybrid configuration is utilized to discuss energy harvesting by a cantilever beam and prismatic-shaped cylinder subjected to wind flow from transverse direction, by using a special class of aeroelastic oscillations known as galloping. After establishing the importance of accurate modeling of aeroeolastic galloping force, we proceed on to discuss about hybrid energy harvesting. The inclined square section cylinders are investigated to harvest aeroelastic energy offered by galloping oscillations using accurate modeling proposed in the first part, again by using a hybrid configuration. The last part of harvesting energy by galloping oscillation using a hybrid transduction mechanism deals with using the same cantilever based hybrid galloping harvester, but this time by inclusion of a non-rigid support exhibiting non-zero slope. The impact of such support on piezoelectric and electromagnetic energy harvesting is investigated in detail. The second part of this dissertation deals with using the same hybrid configuration for harnessing aeroelastic energy by using another, rather well-known class, named vortex-induced vibrations. The different tools of nonlinear dynamics and vibrations, such as Galerkin discretization, Normal form of Hopf bifurcation, and shooting method are used to dissect the hybrid energy harvesters in length throughout the Dissertation. It is concluded at the end that hybrid energy harvesters come with their own added shunt damping effects because of an additional transducer to a single functioning transducer, whether an added piezoelectric layer or an electromagnet-inductive coil. At the same time, careful selection of the electrical load resistances of respective piezoelectric and electromagnetic circuitries would interplay with each other, can help bring the overall coupled damping of hybrid formation to acceptable reduced levels. This careful selection can help replace a sole classical electromagnetic or piezoelectric harvester with a hybrid one which can power multiple electronic lower power gadgets.