This introductory chapter presents the state of the art in the multidisciplinary research field of asbestos and mineral fibres in general. The book describes the world of mineral fibres with its huge complexity and poorly understood, detrimental bio-chemical interaction with the human body. The approach of the chemist/mineralogist/crystallographer adopts the perspective of the fibre itself (the invader of the body) whereas the approach of the bio-chemist/toxicologist/physician adopts the perspective of the organism (the invaded) interacting with the fibre. Both perspectives must be considered in synergy in an attempt to outline a conclusive model explaining the toxicity of mineral fibres, and provide a robust scientific basis that can be used by political and social partners to resolve finally the global issue of asbestos.