Magnetic resonance imaging (MRI) provides exquisite depiction of anatomy and function without the ionizing radiation found in e.g. CT or PET. However, significant drawbacks still exist. This is primarily due to the limited speed and signal-to-noise ratio (SNR) of MRI, and most important, the fact that these two quantities are linked to each other. Conventionally, as with any linear system, any increase in imaging speed has required a loss in SNR and vice versa. In order to realize any truly dramatic increases in either SNR or imaging time, some way to break this relationship must be found. New developments in the world of information theory, such as Compressed Sensing (CS), have completely changed the landscape of medical imaging forever and have in particular forced us to completely rethink the way in which we acquire and process data for MRI. In this new era of MR imaging, the focus of an MR acquisition has rapidly evolved from simply collecting images to directly collecting information. In particular, in this lecture, we will discuss three classes of acquisitions that have been dramatically impacted by these methods. The first class of applications consists of images that are intrinsically sparse, such as MR angiography, where most of the volume of data is near zero-valued. Here, we have achieved acquisition speed-ups of over 400x. The second class comprises model-based acquisitions, wherein we can for example, assume something about the dynamic timecourse of the data that is constrained by quantum mechanics. Finally, the third class utilizes the vast array of images stored in electronic repositories to improve the image quality, especially in longitudinal studies. We will highlight several examples where these new methods have dramatically improved both the SNR and temporal resolution of MR images beyond all previously established limits which provides clinically useful exams in dramatically reduced time with increased SNR.