In this thesis, a theoretical approach is applied to study active matter systems. First, we investigate the collective behavior of linearly connected active Brownian particles within the framework of an analytic theory approach, and, second, we analyse the swimming characteristics of bacteria, such as E. coli, by means of computer simulations. We find a distinct influence of motility on semiflexible filaments. A chain of active particles results in more than just the sum of its parts and gives rise to novel phenomena. In particular, activity strongly influences the conformational properties. We find that flexible filaments stretch with increasing activity, whereas rather stiff filaments are softened due to the activity, which then leads to a contraction of the chain for intermediate activities. However, beyond a certain threshold, the filament starts to swell again, but in a flexible-chain-like manner. Moreover, activity changes drastically the relaxation behavior and, hence, the dynamics of the filament. Furthermore, hydrodynamic interactions change via the coupling with the activity the conformation of the chain, in contrast to passive polymers. Thereby, it appears to be important whether the activity is an intrinsic property of the chain, or is induced by an external field. Also the dynamics is strongly influenced by the hydrodynamic interactions and shows a distinctly different behaviour compared to a passive polymer in dilute solution. We study the swimming behavior of bacterial swarmer cells using a detailed simulation model for the bacterial body and the flagella. The embedding fluid is modelled via the multiparticle collision dynamics simulation approach. We consider fluid films of different thicknesses, and cells with various arrangements of flagella. Overall, we find rather heterogeneous flagellar bundle conformations and cell dynamics. Specifically, confinement influences the bundle structure and the swimming pattern of the cell. Thereby, we find a transition from curved to straight swimming trajectories for surface-separation distances below trice the body diameter. In addition, we find a slight increase of the swimming speed in narrow slits. Contrary to experimental observation, we find a lower migration speed for swarmer cells compared to planktonic swimmer cells. This aspect needs further investigations. Moreover, we study a raft of P. mirabilis-like swarmer cells, a bacterial strain of cells with extremely elongated bodies and hundreds of flagella. Thereby, we focus on cell-cell interactions, specifically on the inter-cell flagellar bundle formation. We find, for the first time using computer simulations bundling of flagella belonging to adjacent cells
