Abstract: In this panoramic talk, we shall provide an overview of Poisson geometry and some recent results obtained by the speaker and collaborators. First, we shall present the key definitions and concepts, and relate them to their foundationalmotivations in relation to both classical and quantum mechanics. Secondly, we shall describe some results including the description of symplectic realizations and their application to both numerical approximation of Hamiltonian ODEs and to Kontsevich's quantization formula.