Al-Sc alloys are promising light-weight materials that possess excellent mechanical properties. These properties critically depend on the size and distribution of Al3Sc particles that precipitate out from a Sc supersaturated solid solution. In this work we investigate the thermodynamics and kinetics of these precipitates, which are both crucial to understanding their structure and stability. We address the thermodynamic properties of Al3Sc by including all the relevant finite-temperature contributions in a first-principles approach. In particular, we address the experimentally observed low-temperature phenomena in the heat capacity, such as the importance of electronic excitations and the origin of a boson peak in the vibrational contributions. The precipitation kinetics is studied in terms of fully atomistically derived time-temperature-transformation (TTT) diagrams employing kinetic Monte-Carlo simulations. The derived features in the TTT diagrams can be used to design processing routes that tailor the size of precipitates in Al-Sc alloys.