The penetration of devices integrated with location-based services and internet services has generated massive data about the everyday life of citizens and tracked their activities happening in cities. Crowdsourced data, such as social media data, POIs data and collaborative websites, generated by the crowd, has become fine-grained proxy data of urban activity and widely used in research in urban studies. However, due to the heterogeneity of data types of crowdsourced data and the limitation of previous studies mainly focusing on a specific application, a systematic review of crowdsourced data mining for urban activity is still lacking. In order to fill the gap, this paper conducts a literature search in the Web of Science database, selecting 226 highly related papers published between 2013 and 2019. Based on those papers, the review firstly conducts a bibliometric analysis identifying underpinning domains, pivot scholars and papers around this topic. The review also synthesises previous research into three parts: main applications of different data sources and data fusion; application of spatial analysis in mobility patterns, functional areas and event detection; application of socio-demographic and perception analysis in city attractiveness, demographic characteristics and sentiment analysis. The challenges of this type of data are also discussed in the end. This study provides a systematic and current review for both researchers and practitioners interested in the applications of crowdsourced data mining for urban activity.