Messenger RNA (mRNA) therapeutics have garnered considerable attention due to their remarkable efficacy in the treatment of various diseases. The COVID-19 mRNA vaccine and RSV mRNA vaccine have been approved on the market. Due to the inherent nuclease-instability and negative charge of mRNA, delivery systems are developed to protect the mRNA from degradation and facilitate its crossing cell membrane to express functional proteins or peptides in the cytoplasm. However, the deficiency in transfection efficiency and targeted biological distribution are still the major challenges for the mRNA delivery systems. In this review, we first described the physiological barriers in the process of mRNA delivery and then discussed the design approach and recent advances in mRNA delivery systems with an emphasis on their tissue/cell-targeted abilities. Finally, we pointed out the existing challenges and future directions with deep insights into the design of efficient mRNA delivery systems. We believe that a high-precision targeted delivery system can greatly improve the therapeutic effects and bio-safety of mRNA therapeutics and accelerate their clinical transformations. This review may provide a new direction for the design of mRNA delivery systems and serve as a useful guide for researchers who are looking for a suitable mRNA delivery system.