In this talk, we will present some mathematical models for mosquito and pest populations and present some results concerning their dynamics and optimal and feedback control strategies. We will mostly concentrate on models for the Sterile Insect Technique (SIT) but also briefly mention the Wolbachia population replacement strategy for mosquitoes. We will consider both Ordinary Differential Equation models and spatial models described by systems of reaction-diffusion Partial Differential Equations (PDE).