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Massive multiple-input multiple-output is a promising physical layer technology for 5G wireless communications due to its capability of high spectrum and energy efficiency, high spatial resolution, and simple transceiver design. To embrace its potential gains, the acquisition of channel state information is crucial, which unfortunately faces a number of challenges, such as the uplink pilot contamination, the overhead of downlink training and feedback, and the computational complexity. In order to reduce the effective channel dimensions, researchers have been investigating the low-rank (sparse) properties of channel environments from different viewpoints. This paper then provides a general overview of the current low-rank channel estimation approaches, including their basic assumptions, key results, as well as pros and cons on addressing the aforementioned tricky challenges. Comparisons among all these methods are provided for better understanding and some future research prospects for these low-rank approaches are also forecasted.