Incomplete data sampling is an attractive approach to accelerate MRI but it requires prior knowledge-driven image reconstruction. Sparsity is a powerful concept that allows linking many different types of prior knowledge to the mathematical apparatus adopted in MR image reconstruction. Compressed sensing theory establishes conditions for optimal use of sparse representations for high quality MR image reconstruction from undersampled data. In this talk, we will cover the aforementioned concepts of advanced image reconstruction and demonstrate real examples of accelerated structural and dynamic MRI. We will also discuss both theoretical requirements of compressed sensing and essential aspects of its practical implementation.