It has been proven that advanced building control, like model predictive control (MPC), can notably reduce the energy use and mitigate greenhouse gas emissions. However, despite intensive research efforts, the practical applications are still in the early stages. There is a growing need for multidisciplinary education on advanced control methods in the built environment to be accessible for a broad range of researchers and practitioners with different engineering backgrounds. This paper provides a unified framework for model predictive building control technology with focus on the real-world applications. From a theoretical point of view, this paper presents an overview of MPC formulations for building control, modeling paradigms and model types, together with algorithms necessary for real-life implementation. The paper categorizes the most notable MPC problem classes, links them with corresponding solution techniques, and provides an overview of methods for mitigation of the uncertainties for increased performance and robustness of MPC. From a practical point of view, this paper delivers an elaborate classification of the most important modeling, co-simulation, optimal control design, and optimization techniques, tools, and solvers suitable to tackle the MPC problems in the context of building climate control. On top of this, the paper presents the essential components of a practical implementation of MPC such as different control architectures and nuances of communication infrastructures within supervisory control and data acquisition (SCADA) systems. The paper draws practical guidelines with a generic workflow for implementation of MPC in real buildings aimed for contemporary adopters of this technology. Finally, the importance of standardized performance assessment and methodology for comparison of different building control algorithms is discussed.