Low rank model arises from a wide range of applications, including machine learning, signal processing, computer algebra, computer vision, and imaging science. Low rank matrix recovery is about reconstructing a low rank matrix from incomplete measurements. In this survey we review recent developments on low rank matrix recovery, focusing on three typical scenarios: matrix sensing, matrix completion and phase retrieval. An overview of effective and efficient approaches for the problem is given, including nuclear norm minimization, projected gradient descent based on matrix factorization, and Riemannian optimization based on the embedded manifold of low rank matrices. Numerical recipes of different approaches are emphasized while accompanied by the corresponding theoretical recovery guarantees. This is an ill-posed problem without assuming any structure on X since there are more unknowns than equations. However, noticing that the number of degrees of freedom in an n by n rank r matrix is p2n´rqr [100] which can be much smaller than n 2 provided r is small, it is reasonable to expect to reconstruct a low rank matrix from fewer than n 2 measurements.Authors are listed alphabetically.