Microalgae are photosynthetic microorganisms with a high biotechnological potential. They have many industrial applications, including biofuel and wastewater treatment. Nevertheless, controlling optimal growth conditions for full-scale outdoor cultivation of microalgae is challenging. Mathematical models based on differential equations are of great help to better manage these nonlinear and dynamical systems. The aim of this thesis is to better understand how different factors such as the availability of light and nutrients affect microalgae growth in high density cultures. In a first part, we study the impacts of photo-inhibition and medium turbidity when microalgae growth is only limited by light. Then, we analyse the long-term behaviour of a microalgae population accounting both for nutrient and light limitations. We determine the conditions to avoid population extinction. In particular, we show that continuous periodic culture operation (periodic dilution rate and nutrient supply) under periodic fluctuations of environmental conditions (such as the light source or temperature) leads to a periodic behavior. In a third part, we show how to maximize microalgae productivity. We determine a strategy for shading outdoor cultures to protect microalgae from excess light. We also find the optimal incident light for photobioreactors operated at steady state. In the context of wastewater treatment, we determine numerically the optimal depth of a culture limited by light and nutrient. Finally, the last part of this work proposes and validates a mathematical model accounting for light, nitrogen, and phosphorus limitations, including photoacclimation dynamics.