Bone was a crucial biological material for the evolution of large terrestrial organisms and is today essential for most of our daily activities and well-being. From an engineering perspective, this living material features highly desirable properties for modern load-bearing structures. It is made of abundant and environmental-friendly building blocks, which are combined into a tough and durable structure that can continuously modify itself to adapt to changes in the mechanical load imposed by the surroundings. In this review article, we compile and discuss scientific findings that allow us to understand bone as a complex system with properties that emerge from cell-mediated interactions of molecules and particles at multiple length scales. Analogous to other complex systems, such interactions lead to self-organization, hierarchical structures and adaptive behavior without the need of a central controlling unit. A rich range of physical, chemical and biological phenomena provide a framework for information to be generated and processed in this complex system. Understanding the interplay between such underlying phenomena and their emerging properties should help the diagnosis and treatment of bone-related medical conditions and might provide guidelines for the future development of more sustainable materials and engineering structures.