The circular economy (CE) paradigm can eradicate the problems caused by the traditional linear economic approach adopted by the building industry. But the efforts to implement CE in the building and construction industry are fragmented and lack consensus. If improved, the ability to measure and report on progress can help in effectively transiting to CE. In this regard, wide-ranging building circularity indicators (C-indicators) have been proposed. However, the extant literature highlights that the comprehensive research on existing CE assessment tools in the building industry is still lacking, while policymakers (e.g., European Commission) and standards (e.g., ISO) have emphasized the need for a universally recognized circularity framework for buildings. To help this cause, this review inventories and critically analyzes 35 existing tools through an extended systematic literature review of 51 carefully selected documents from both academic and grey literature. It is found that there is a sharp increase in publications in recent years, with Europe leading the way. Along with the academic community, government agencies and consulting companies have also developed several C-indicators. The content analysis suggests that most indicators are quantitative and can vary in terms of the scale of application, the adopted CE scope and definition, and the underlying key performance indicators (KPIs). The descriptive analysis reveals that most indicators are in the developing stage and substantially stress recycling and reuse, overlooking some important aspects like energy, emission, and water. Innovative technical solutions like the design for adaptability and disassembly are excessively used to measure the circular potential of structures. The existing sustainability and circularity tools are seen as a good starting point for developing new frameworks. This extensive review and critical analysis provide a synthesis and explanation of the developing research theme of building C-indicators and highlight the remaining key challenges. The findings can drive the standardization of a universally accepted framework.