For decades, scientists have been investigating how human activity, like fluid injection or extraction, deep underground mining, quarrying and impoundment of reservoir behind dams, can influence or stimulate seismicity in a region. The topic gained more attention in the early 1960s, when hundreds of quakes were recorded in Colorado after fluid had been injected into a disposal well near the Rocky Mountain Arsenal. In this category of stimulated earthquakes, reservoir-triggered earthquakes are the most common. Ambient and reservoir stresses and pore pressure jointly control the stability of faults near a reservoir. The stresses and pore pressure induced by a reservoir are miniscule in comparison with the ambient crustal stresses in the hypocentral regions of earthquakes. When the ambient stresses approach critical levels for failure of an upper crustal fault, the reservoir-induced stresses and pore pressure may exert influence by assisting or opposing the attainment of criticality. Mathematical developments in porous elastic theory and concepts of Coulomb stress have become important tools to understand reservoir-triggered earthquakes. Detailed numerical simulations of earthquakes in the vicinity of various dams and reservoirs are discussed by using the above tools.