Damages in rotor systems have severe impact on their functionality, safety, running durability and their industrial productivity, which usually leads to unavoidable economical and human losses. Rotor systems are employed in extensive industrial applications such as jet engines, gas and steam turbines, heavy-duty pumps and compressors, drilling tools, and in other machineries. One of the major damages in such systems is the propagation of fatigue cracks. The heavy-duty and recurrent cyclic fatigue loading in rotor systems is one of the main factors leading to fatigue crack propagation. For the past few decades, numerous research have been conducted to study crack related damages and various methodologies were proposed or employed for damage detection in rotor systems. Therefore, the purpose of the present review article is to provide a thorough analysis and evaluation regarding the associated research related to the modeling aspects of rotor systems that are associated with various kinds of (rotor related) damages. Based on this review, it is observed that the crack modeling, especially with the breathing crack type in rotor systems, is still based on few primary models. Several researchers, based on different assumptions, have extended and modified such models to be more reliable for analysis. Moreover, the arising demand for early crack detection has led to utilization of various tools such as Fast Fourier transform, Hilbert Huang transform, wavelet transform, whirling analysis, energy methods, and the correlation between backward whirling and rotor faults etc. In addition, the significant impact of nonsynchronous whirl within resonance zones of rotor systems on post-resonance backward whirl, under various rotor related faults, is also highlighted in the present review. Therefore, the review provides an evaluation and comparison between several crack models and detection methodologies in rotor systems. Moreover, this review could help in identifying the gaps in modeling, simulation, and dynamical analysis of cracked rotor systems to establish robust research platform on cracked rotor systems.