Over the past decades, robotics has shown great potential to impact the built environment, from automation to differentiation and efficient construction. However, construction processes are highly complex and require tackling a multitude of problems, from safety and robustness to ease of control and interactivity. For this reason, the field of construction robotics is still evolving, requiring finding solutions for new challenges every day. The present review analyzes the role of robotics in construction and architecture over time and highlights current trends in shifting from pure automation toward collaborative and adaptive processes that have the potential to fully integrate robotics into a rigid and challenging industry, such as construction. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 14 is May 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.