Microscopy is an essential tool in medicine and biomedical research. Traditional microscopes rely on bulky optics, complicating their usage when studying live animal tissues. In addition, light cannot penetrate very far in most biological tissues due to scattering, so typically only superficial tissues can be accessed non-invasively. In this thesis, microscopic imaging was achieved through a single multimode optical fiber. Fibers are extremely thin (less than 300 µm) and guide light efficiently, so they provide a minimally invasive solution for microscopic imaging at any depth inside tissues. Imaging via single fibers requires compensation of modal scrambling, an effect that distorts images in multimode fibers. The tool used in this thesis to control light and undo modal scrambling is the transmission matrix, a general framework that can describe the input-output relationship of any optical system very precisely. A procedure was developed to measure large transmission matrices accurately, based on digital holography and wavefront shaping with spatial light modulators. High-resolution image transmission through single fibers was subsequently demonstrated in a variety of configurations. Building on these results, confocal imaging was implemented in order to increase image contrast. Finally, the bending tolerance was investigated, and a set of conditions was identified under which fibers can be deformed without losing significant imaging performance. Multimode fiber imaging is a promising solution for endoscopic microscopy. By compensating modal scrambling, it is possible to turn fibers into extremely thin microscopes with diffraction-limited resolution. This could be applied for example to assist in biopsies or for other minimally invasive imaging applications.