The direct-detection optical fiber communication system has become the main solution for the future short-reach optical transmission links due to its simple structure and low cost. The field-signal recovery (FSR) technique is a critical technique to improve the capacity of the direct-detection system. This paper introduces a system structure, working principle and main research progress of Stokes vector receiver, carrier-assisted differential detection receiver and Kramers-Kronig (KK) receiver in direct detection optical fiber communication systems. The advantages and disadvantages of three commonly used FSR techniques are compared. The results show that compared with the other two techniques, and the KK receiver technology has obvious advantages. Finally, the important position of KK receiver in the future direct-detection optical fiber communication systems is clarified. Meanwhile, the key technical challenges faced by KK receiver are analyzed and the solutions for reference are given ultimately.