Nowadays, with advanced information technologies deployed citywide, large data volumes and powerful computational resources are intelligentizing modern city development. As an important part of intelligent transportation, route recommendation and its applications are widely used, directly influencing citizens` travel habits. Developing smart and efficient travel routes based on big data (possibly multi-modal) has become a central challenge in route recommendation research. Our survey offers a comprehensive review of route recommendation work based on urban computing. It is organized by the following three parts: 1) Methodology-wise. We categorize a large volume of traditional machine learning and modern deep learning methods. Also, we discuss their historical relations and reveal the edge-cutting progress. 2) Application\-wise. We present numerous novel applications related to route commendation within urban computing scenarios. 3) We discuss current problems and challenges and envision several promising research directions. We believe that this survey can help relevant researchers quickly familiarize themselves with the current state of route recommendation research and then direct them to future research trends.