Memories occupy most of the silicon area in nowadays' system-on-chips and contribute to a significant part of system power consumption. Though widely used, nonvolatile Flash memories still suffer from several drawbacks. Magnetic random access memories (MRAMs) have the potential to mitigate most of the Flash shortcomings. Moreover, it is predicted that they could be used for DRAM and SRAM replacement. However, they are prone to manufacturing defects and runtime failures as any other type of memory. This article provides an up-to-date and practical coverage of MRAM test and reliability solutions existing in the literature. After some background on existing MRAM technologies, defectiveness and reliability issues are discussed, as well as functional fault models used for MRAM. This article is dedicated to a summarized description of existing test and reliability improvement methods developed so far for various MRAM technologies. The last part of this article gives some perspectives on this hot topic.