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This paper aims to give a general and unifying presentation on modeling of wheel mobile robots (WMRs) in the presence of wheel skidding and slipping from the perspective of control design. We present kinematic models that explicitly relate perturbations to the vehicle skidding and slipping. Four configurations of mobile robots are considered, and perturbations due to skidding and slipping are categorically classified as input-additive, input multiplicative, and/or matched/unmatched perturbations. Furthermore, we relate the WMR's maneuverability with the vehicle controllability that provides a measure on the WMR ability to track a trajectory in the presence of wheel skidding and slipping. These classifications and formulations lay a base for the deployments of various control design techniques to overcome the addressed perturbations.