Magnetic Resonance Imaging (MRI) plays a vital role in diagnosis, management and monitoring of many diseases. However, it is an inherently slow imaging technique. Over the last 20 years, parallel imaging, temporal encoding and compressed sensing have enabled substantial speed-ups in the acquisition of MRI data, by accurately recovering missing lines of k-space data. However, clinical uptake of vastly accelerated acquisitions has been limited, in particular in compressed sensing, due to the time-consuming nature of the reconstructions and unnatural looking images. Following the success of machine learning in a wide range of imaging tasks, there has been a recent explosion in the use of machine learning in the field of MRI image reconstruction.A wide range of approaches have been proposed, which can be applied in k-space and/or image-space.Promising results have been demonstrated from a range of methods, enabling natural looking images and rapid computation.In this review article we summarize the current machine learning approaches used in MRI reconstruction, discuss their drawbacks, clinical applications, and current trends.