Magnetic Resonance Imaging (MRI) is a non-invasive medical imaging modality that is widely used by clinicians and researchers to picture body anatomy and neuronal function. However, long scan time remains a major problem. Recently, multiple techniques have emerged that reduce the acquired MRI signal samples, hence dramatically accelerating the acquisition. These techniques involve sophisticated signal reconstruction procedures that in essence require solving regularized optimization problems, and clinical adoption of accelerated MRI critically relies on self-tuning solutions for these problems. Further to this, recent experimental approaches in cognitive neuroscience favor employing naturalistic audio-visual stimuli that closely resemble humans’ daily-life experience. Yet, these modern paradigms inevitably lead to huge functional MRI (fMRI) datasets that require advanced statistical and computational techniques to uncover the large amount of embedded information. Here, we propose a novel efficient datadriven self-tuning reconstruction method for accelerated MRI. We demonstrate superior performance of the proposed method across various simulated and in vivo datasets and under various scan configurations. Furthermore, we develop statistical analysis tools to investigate the neural representation of hundreds of action categories in natural movies in the brain via fMRI, and study their attentional modulations. Finally, we develop a model-based framework to estimate temporal extent of semantic information integration in the brain, and investigate its attentional modulations using fMRI data recorded during natural story listening. In short, the methodological and analytical approaches introduced in this thesis greatly benefit clinical utility of accelerated MRI, and enhance our understanding of brain function in daily life.