The difficulty in visualizing unstained biological cells using brightfield microscopy has resulted in the development of several specialized imaging techniques that can enhance the contrast of subcellular features without the need for labeling. Examples include phase contrast, differential interference microscopy, dark field microscopy, and Rheinberg illumination. However, these techniques are qualitative in nature and do not provide any direct measurement of cellular morphology in terms of thickness or refractive index. Quantitative phase imaging refers to a set of emerging methods with the potential to provide quantitative real-time measurement of the phase delay introduced by the specimen with nanometric accuracy and with the same spatial resolution afforded by brightfield microscopy. Quantitative phase imaging, therefore, provides a powerful means to study cellular dynamics. Several methods exist for implementing quantitative phase imaging, which include coherent approaches based on interferometry known as digital holographic microscopy. Digital holographic microscopy is an optic-electronic technique that enables the numerical reconstruction of the complex wave-field reflected from, or transmitted through, a target with a single capture. Together with phase unwrapping, this method permits a height profile, a thickness profile, and/or a refractive index profile, to be extracted, in addition to the reconstruction of the image intensity. Digital holographic microscopy is unlike classical imaging systems in that one can obtain the focused image without situating the camera in the focal plane; indeed, it is possible to recover the complex wave-field at any distance from the camera plane. Therefore, the focus distance from the image plane to the camera plane can be estimated automatically by using a focus metric. The aim of the work presented in this thesis is to develop novel methods for digital holographic microscopy in order to improve the quantitative analysis of cellular morphology and detect the nucleus in vivo, together with a number of numerical process techniques both in amplitude and phase profile. This thesis includes a number of separate contributions, some relating to novel optical systems that can be used to record the holograms, and some relating to method of processing the recorded holograms in order to generate meaningful images. A low-cost compact portable module is proposed that can be easily integrated with a brightfield microscope in order to record quantitative phase images. This is the first of two contributions on novel methods to optically record digital holograms. The second optical system that is proposed is a novel optical architecture for off-axis digital holographic microscopy, which allows for continuous change in magnification and numerical aperture by simply moving the sample. There are also three separate contributions that deal with numerical methods for the reconstruction of images recorded using digital holographic microscopy. The first relates to a thorough examination of the potential for sparsity metrics to be used for autofocusing in digital holographic microscopy. The last two contributions both relate to new image processing techniques for label-free color staining of subcellular features using the quantitative phase image as input. The first method is based on simulated Rheinberg illumination, while the second method is purely digital and can be related to the concept of local spatial frequency in the image. Both are shown to provide high quality color images of diatom cells.