This dissertation investigates the influence of geometry on the dynamics of confined microswimmers. We show that the presence of solid boundaries can encourage local accumulation, clustering, and even large-scale collective flows including at moderate concentrations. Following experimental work (either done by us or our collaborators), as well as existing literature, we build theoretical models and simulations based on hydrodynamic singularities and steric interactions with walls and between swimmers. Our models successfully describe the emergence of regions where swimmers accumulate, and the subsequent flow patterns observed in the experimental data. We first present an experimental setup to investigate suspensions of magnetotactic bacteria. The experiments were carried out during a visit to the group of Prof. Kari Dalnoki-Veress (McMaster University). These bacteria synthesize nanomagnets in their cytoplasm and align passively with external magnetic fields as they propel by rotating their back flagellum, and therefore belong to the class of biased pusher swimmers. We investigate the dynamics of dense suspensions of such swimmers in confined geometries in an external field. In a rectangular channel, we observe experimentally the emergence of plumes of bacteria, which merge until they reach a stationary state and create convection-like flow patterns. This new collective motion is modelled by considering the hydrodynamic interactions from the flow from the two opposite forces generated by the propulsion of each bacterium. The confinement by the top and bottom walls promotes attractive interactions between swimmers and sets the long-term flow scale. Existing experiments showed that the collective dynamics of a suspension of biased swimmers in spherical droplets are very different: as often for collective motions in spherical geometries, the flow is a large-scale vortex, but surprisingly, it has a preferred direction orthogonal to the magnetic field. We extend our hydrodynamic model to include swimmer chirality and reorientation, and spherical confinement. We show that the mechanism for the onset of collective motion in a sphere is entirely different when the swimmers have a preferred orientation. The symmetry breaking then stems either from long-range hydrodynamic interactions between populations at opposite magnetic poles, from local swimmer-wall interactions, or a combination of the two mechanisms. Using again a model based on hydrodynamic singularities and their images with respect to no-slip walls, we then study the possibility of hydrodynamic clustering for swimmers at a boundary, where swimmer encounters are more likely, but this time without an external director field. We consider a classic representation for spherical swimmers inducing slip velocities at their surface, the squirmer model. We focus on symmetric boundary-mediated encounters of weak squirmers under gravity, in the far-field as well as in the lubrication regime. The far-field analysis predicts that most reorientation occurs after contact, so we focus on the near-field reorientation of circular groups of squirmers. We show that a large number of swimmers and the presence of gravity can stabilise clusters of pullers, while the opposite is true for pusher swimmers; to be stable, clusters of pushers would thus need to be governed by other interactions, for example phoretic. Finally, while hydrodynamic interactions are essential to understand the above-mentioned dynamics of confined microswimmers, they can be subdominant compared to steric interactions, especially if the confinement geometry is more complex. We show that it is the case for motile Chlamydomonas algae in two-dimensional chambers reproducing sections of foam Plateau borders. The group of Prof. Florence Elias (Université Paris Diderot) had previously observed that these cells swim preferentially in the corners of the chamber. We build a geometrical billiard model with a constant scattering angle that leads to corner accumulation. Including empirical data from the experiments of our collaborators, in particular, the distribution of scattering angles enables us to reproduce the experimental probability density function of a swimmer in the chamber. In this system, hydrodynamic interactions only set the speed of the algae, but not their trajectories, and it is instead the interplay of motility and contact interaction that leads to trapping in this geometry.