In the presence of a target, tree failures have the potential to damage property, disrupt services, or threaten public safety. Worldwide, several qualitative methods have been developed to provide a systematic approach for tree risk assessment and management. The consistency and accuracy of these methods, the values placed on the tree in question and its potential targets, and the risk perceptions and levels of acceptance of the evaluator and tree owner all influence how risk is managed. This review explores the concept of risk, examines and contrasts the most commonly referenced tree risk assessment methods, and summarizes research on public perceptions of trees and the risk of trees and greenspaces in built environments. The review identifies general summarized themes and gaps in the available literature to guide future research.