Eukaryotic cells use a multitude of protein machines to regulate their own structure. In this thesis, we study how the geometrical arrangement of these interacting microscopic active elements sculpt the cell's own internal microstructure and its membrane enclosure.We first focus on the mechanisms generating actomyosin contractility, a crucial driver of cell motion and organization. We question the current position of highly organized, sarcomeric contractility as the only possible mechanism to drive contractility. We propose an alternative mechanism, and show that only it can account for the observed contractility of disordered actomyosin assemblies. It moreover yields qualitatively new effects in intracellular force transmission, including stress reversal and amplification, consistent with experimentally observations in fiber networks.We next elucidate some of the mechanisms through which the cell deforms and cuts its own membrane, thus enabling exchanges with the extracellular medium as well as between its internal compartments. We find that the function of the proteins responsible for this remodeling is strongly influenced by the mechanics of the membrane, and use these effects to elucidate the modes of operation of proteins clathrin and dynamin, as well as of protein complex ESCRT-III