Structural optimization within concrete construction has been increasingly taken up in research within the last two decades. Possible drivers are the need for material-reduced and thus resource-efficient structures as well as recent advancements in automated concrete construction. However, structural concrete is characterized by nonlinear material behavior. Consequently, the merge of structural concrete design and topology optimization is not trivial. This paper reviews and assesses the topic of topology optimization within concrete construction, carrying out an extensive quantitative as well as qualitative review on practical and numerical applications. The following research areas are identified: Multimaterial modeling, stress constraints, concrete damage modeling, strut and tie modeling, combined truss-continuum topology optimization, the consideration of multiple load cases, a focus on construction techniques and alternative approaches. Although the number of research papers dealing with the topic of topology optimization in concrete construction is numerous, there are only few that actually realized topology optimized concrete structures. In addition, only a little number of experiments was performed for an objective evaluation of the found geometries so far. Concluding this review, a list of future challenges, like the incorporation of sustainability measurements within the optimization process, is given and thus serves as a guidance for subsequent research.