The impact is one of the most abundant phenomena in the field of multi-body dynamics when two or more bodies come in close vicinity and depending on the interaction properties and geometry, all the interacting bodies experience certain impulsive force for an infinitesimal duration. Nowadays, impact modelling becomes an intrinsic part in the modelling of structural pounding, granular materials, crash and machinery analysis, robotics and bio-mechatronics applications. Since the time of Newton, numerous literatures have been published on the modelling of both normal and oblique contact phenomena. The scope of this critical review is limited to consolidate the existing knowledge on the computational model of normal directional impact on rigid bodies. The literature related to modelling of oblique impact, soft body impact, impact damage in composites and associated stress wave propagation are excluded from the scope of this critical review. Smooth and non-smooth mechanics are two schools of thought in simulating the normal directional impact. In this review, the shortcomings of all the classes of compliance and non-smooth models are analysed in the unified dimensionless frame-work to compare their response output with the conventional stereo-mechanical model. This review opens a new avenue for future researchers in selecting a proper contact formulation for specific application. [ABSTRACT FROM AUTHOR]