Monte Carlo calculations in field theory/many-body systems are frequently plagued by the so called sign-problem. It obstructs calculation of finite density QCD, the Hubbard model away from half-filling and all real time calculations. We discuss a new approach to address the sign problem.  It is based on deforming the domain of integration into complex field space. We will argue that for conceptual and numeric reasons it may be advantageous not to use the steepest descent manifolds (thimbles) as it was originally suggested. We will discuss a variety of algorithms based on the holomorphic flow, neural nets and physically motivated ansatze and their application to fermionic field theories, gauge theories  and quantum mechanical models, including real time dynamics.