Green space is increasingly recognized as an important component of the urban environment. Adequate management and planning of urban green space is crucial to maximize its benefits for urban inhabitants and for the urban ecosystem in general. Inventorying urban vegetation is a costly and time-consuming process. The development of new remote sensing techniques to map and monitor vegetation has therefore become an important topic of interest to many scholars. Based on a comprehensive survey of the literature, this review article provides an overview of the main approaches proposed to map urban vegetation from high-resolution remotely sensed data. Studies are reviewed from three perspectives: (a) the vegetation typology, (b) the remote sensing data used and (c) the mapping approach applied. With regard to vegetation typology, a distinction is made between studies focusing on the mapping of functional vegetation types and studies performing mapping of lower-level taxonomic ranks, with the latter mainly focusing on urban trees. A wide variety of high-resolution imagery has been used by researchers for both types of mapping. The fusion of various types of remote sensing data, as well as the inclusion of phenological information through the use of multi-temporal imagery, prove to be the most promising avenues to improve mapping accuracy. With regard to mapping approaches, the use of deep learning is becoming more established, mostly for the mapping of tree species. Through this survey, several research gaps could be identified. Interest in the mapping of non-tree species in urban environments is still limited. The same holds for the mapping of understory species. Most studies focus on the mapping of public green spaces, while interest in the mapping of private green space is less common. The use of imagery with a high spatial and temporal resolution, enabling the retrieval of phenological information for mapping and monitoring vegetation at the species level, still proves to be limited in urban contexts. Hence, mapping approaches specifically tailored towards time-series analysis and the use of new data sources seem to hold great promise for advancing the field. Finally, unsupervised learning techniques and active learning, so far rarely applied in urban vegetation mapping, are also areas where significant progress can be expected.