Wound healing is essential for the restoration of the barrier function of the skin. During this process, cells at the wound edges proliferate and migrate, leading to re-epithelialization of the wound surface. Wound healing assays are used to study the molecular mechanisms of wound repair, as well as in the investigation of potential therapeutics and treatments for improved healing. Numerous models of wound healing have been developed in recent years. In this review, we focus on in vitro assays, as they allow a fast, cost-efficient and ethical alternative to animal models. This paper gives a general overview of 2-dimensional (2D) cell monolayer assays by providing a description of injury methods, as well as an evaluation of each assay's strengths and limitations. We include a section reviewing assays performed in 3-dimensional (3D) culture, which employ bioengineered skin models to capture complex wound healing mechanics like cell-matrix interactions and the interplay of different cell types in the healing process. Finally, we discuss in detail available software tools and algorithms for data analysis.