Releases of sterile mosquitoes have been an effective weapon to fight malaria and other mosquito-borne diseases. To study the impact of these mosquitoes interacting with wild mosquitoes on the diseases transmission, we formulate continuous-time or discrete-time mathematical models, based on differential equations or difference equations, for the interactive dynamics of wild and sterile mosquitoes. We consider different strategies in releasing sterile mosquitoes. With fundamental analysis of the model equations, we investigate their interactive dynamics and compare the impact of different releasing strategies. We demonstrate the rich dynamical features of the models by numerical examples as well.