As fluids are injected into a reservoir, the pore fluid pressure changes in space and time. These changes induce a mechanical response to the reservoir fractures, which in turn induces changes in stress and deformation to the surrounding rock. The changes in stress and associated deformation comprise the geomechanical response of the reservoir to the injection. This response can result in slip along faults and potentially the loss of fluid containment within a reservoir as a result of cap-rock failure. It is important to recognize that the slip along faults does not occur only due to the changes in pore pressure at the fault location; it can also be a response to poroelastic changes in stress located away from the region where pore pressure itself changes. Our goal here is to briefly describe some of the concepts of geomechanics and the coupled flow-geomechanical response of the reservoir to fluid injection. We will illustrate some of the concepts with modeling examples that help build our intuition for understanding and predicting possible responses of reservoirs to injection. It is essential to understand and apply these concepts to properly use geomechanical modeling to design geophysical acquisition geometries and to properly interpret the geophysical data acquired during fluid injection.