The last few decades have seen a faster development of digital systems for observing the mobility of people and goods. Various sensing systems - such as radio communication, Wi-Fi, Bluetooth, validation of smart cards, mobile phone, and road traffic monitoring systems - have enabled researchers and practitioners to acquire large amounts of data, which generally refer to individual and collective trajectories. The mobility data can be further enriched with side information, such as text corpora from social media, survey data, and weather information. These massive data, temporally and spatially structured, can benefit from advanced machine learning and data mining methods, providing decision aid tools, and contributing to the development of safer, cleaner, and more efficient transportation systems. They can also help to implement new mobility services for the user. This article provides an overview of methodological advances in temporal and spatial mobility data processing.