Active matter systems are continuously consuming energy from the environment to achieve different purposes, thus being inherently out of equilibrium. Living matter systems are a prominent subgroup of active matter, which range over different length scales, such as cytoskeleton structure, swimming and swarming bacteria, schools of fish, and flocks of birds. Many living organisms face the challenge of achieving controlled motility. In particular, biological microswimmers are able to move in fluid environments at the microscale. At this length scale, the fluid is inertialess and this has consequences in their swimming strategies. This thesis presents a computational study of the motility of microswimmers. We tackle this study by means of two models with different levels of detail, where the fluid is modeled with a particle-based hydrodynamic mesoscale simulation approach, the Multiparticle Collision Dynamics method. In the first part of the thesis, we analyze the bundle formation process and subsequent swimming properties in Bacillus subtilis-like elongated peritrichous bacterial cells for various surface distributions of flagella, namely random, helical, and ring-like arrangements. We employ a detailed non-tumbling bacterium model which accounts for near-field hydrodynamics. Helical and ring patterns preferentially yield configurations with a single bundle, whereas random anchoring is most likely to form configurations with no clear bundles. Furthermore, V-shaped bundle configurations with at least two bundles occur with an equally low probability for all patterns. Rings yield the smallest average swimming speed independent of the type of bundle, followed by helical arrangements, and largest speeds are observed for random anchoring. In the second part of the thesis, we propose a coarse-grained model based on active dumbbells and polymers to study microswimmer collective interactions mediated by hydrodynamics. The monomeric active unit is modeled by a spherical squirmer, which allows us to control the nature of the propelling unit: a pusher, a neutral swimmer, or a puller. The chains are linked by center-to-center harmonic bonds which do not constraint the squirmer orientations. Overall, we find that the nature of the hydrodynamic interactions established between squirmers produce substantially different dynamics and consequent stationary-state alignment of the propulsion directions with respect to each other. Particularly, pairs of pushers exhibit orders of magnitude smaller swimming efficiency than their pusher counterparts, since pullers align preferentially in an antiparallel manner. In contrast, pusher-puller dumbbells show an asymmetric alignment with respect to each other that leads to helical-like trajectories. In linear assemblies, we find greater effective bending stiffnesses for pushers than for pullers. The distinct differences between polymers comprised of pusher or pullers suggest means to control microswimmer assemblies for future microbot applications.