This chapter is devoted tonovel methods (spinor helicity formalism, on-shell recursion, generalized unitarity), developed in the past 20 years for computing scattering amplitudes, that bypass the traditional workflow (Lagrangian ? Feynman rules ? diagrams ? amplitudes via LSZ formulas). The recurring theme of this approach is to avoid, as much as possible, direct references to the underlying Lagrangian, whose gauge invariance is a source of unnecessary redundancies. This chapter covers both the case of tree-level amplitudes (with some extensions to treat a few examples with scalar particles or fermions) and a few problems about one-loop amplitudes (this is limited to some rather simple examples, since calculating loop amplitudes by hand remains a challenging task, even with modern tools).