Topology optimization (TO) has rapidly evolved from an academic exercise into an exciting discipline with numerous industrial applications. Various TO algorithms have been established, and several commercial TO software packages are now available. However, a major challenge in TO is the post-processing of the optimized models for downstream applications. Typically, optimal topologies generated by TO are faceted (triangulated) models, extracted from an underlying finite element mesh. These triangulated models are dense, poor quality, and lack feature/parametric control. This poses serious challenges to downstream applications such as prototyping/testing, design validation, and design exploration. One strategy to address this issue is to directly impose downstream requirements as constraints in the TO algorithm. However, this not only restricts the design space, it may even lead to TO failure. Separation of post-processing from TO is more robust and flexible. The objective of this paper is to provide a critical review of various post-processing methods and categorize them based both on targeted applications and underlying strategies. The paper concludes with unresolved challenges and future work.