Titanium alloy, an ideal aviation and biomedical material, is generally considered as a typical difficult-to-cut material because of low elastic modulus and poor thermal conductivity. The chip formation of titanium alloy is closely related to the machining efficiency, surface integrity and machining stability during cutting process. Thus, this paper focuses on a comprehensive review of the chip morphology, chip microstructure evolution, numerical simulation and formation mechanism during the machining of conventional and additively manufactured (AM) titanium alloys. First, the effect of different cutting methods (turning, milling, drilling, etc.) and cutting conditions (dry, minimum quantity lubrication (MQL), etc.) on chip morphology has been overviewed in detail. Then, a comprehensive analysis of chip microstructure is conducted from the perspective of deformed shear band, grain evolution and segmentation characteristic. The subsequent simulation of titanium alloy chips is summarized including the verification of proposed constitutive model, investigation of shear instability mechanism and segmented chip geometry. Finally, the chip formation mechanism of conventional and AM titanium alloys is discussed in terms of chip formation theory, theoretical model, machining condition and cutting method. This paper provides a critical review of the current research status of chip features and formation mechanism in machining of conventional and AM titanium alloys. This review facilitates to the high-quality machining of conventional and AM titanium alloys through the deep understanding of chip characteristics and formation mechanism.