Magnetic resonance imaging (MRI) is a powerful medical imaging modality that provides diagnostic information without the use of harmful ionizing radiation. As with any imaging modality, the raw acquired data must undergo a series of processing steps in order to produce an image. During these steps, several problems may arise that impact the quality of the final image. While traditional signal and image processing methods have been employed with great success to address these issues, as the field of deep learning has grown, so too has the research of these methods to address problems in MRI. This thesis, a thesis in two parts, will discuss deep-learning approaches for addressing three common problems in computational MRI: noise, reconstruction, and off-resonance blurring. The first part of the thesis proposes the use of an untrained modified deep decoder network in order to denoise as well as reconstruct MR images. The second part of the thesis investigates the generalizability of a convolutional residual network in its ability to correct for blurring due to off-resonance.