The physics of active matter, and more particularly that of active fluids, is currently undergoing an important effervescence, both from a theoretical and experimental point of view. Some microorganisms have the ability to move in a viscous fluid and their speed can reach several times their size per second, despite the low Reynolds number regime in which they live. Their motion generates amazing collective dynamics; indeed, beyond a certain concentration, we observe in these fluids a transition towards a collective motion that does not correspond to the simple addition of individual motions. Mathematical modeling and numerical simulation are essential tools for understanding these phenomena, and the ability to reproduce and control them is a major challenge. I will present an overview of our work on the modeling and simulation of some of these active fluids, based on a representation of each entity at the microscopic level. We are particularly interested in biological fluids such as micro-swimmer suspensions and bronchial cilia involved in mucociliary transport. Our approach allows to reproduce collective dynamics from a description of individual dynamics, and to study numerically the dependence of different macroscopic quantities on the model parameters. This very rich subject allows to address at the same time questions of modeling, analysis and scientific calculation.