Recently, the seawater and brackish water desalination process have gained widespread attention due to the scarcity of drinking water. Among several membrane distillation (MD) methods for desalination, vacuum membrane distillation (VMD), and direct contact membrane distillation (DCMD) are mostly focused techniques. However, there are several technical issues associated with these techniques that have a negative impact on their performance. The most influential of them are temperature polarization (TP) and concentration polarization (CP) that reduces the permeate flux significantly. A state-of-the-art review is presented to gain a clear understanding of, the impact of both the TP and CP on various performance parameters and methods to overcome these obstacles. The main focus is on the causes of TP and CP, theoretical models, experimental key findings for TP and CP, and their impact on the performance of VMD and DCMD. For DCMD, the value of TPC for channels with spacers falls in the range of 0.9-0.97, whereas for flow channels without spacers, the TPC was in the range of 0.57-0.76. Finally, different methods are discussed to overcome the TP and CP.