¡¡¡¡¡¡¡ HEAD The scopeρ of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, Long-range short range separation to solve the self-interaction error, developments for excited states via the Time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, excited states non-adiabatic dynamics. A number of applications are reviewed, focusing on-(i)-the variety of systems that have been studied ======= The scope of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, schemes to solve the self-interaction error, implementation of long-range short-range separation , treatment of excited states via the time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, non-adiabatic dynamics. A number of applications are reviewed, focusing on-(i)-the variety of systems that have been studied ¿¿¿¿¿¿¿ f70d2388346dfe2c2221fafac6c2d19fb13b68b9 such as small molecules, large molecules and biomolecules, bare or functionalized clusters, supported or embedded systems, and-(ii)-properties and processes, such as vi-brational spectroscopy, collisions, fragmentation, thermodynamics or non-adiabatic dynamics. Finally outlines and perspectives are given.