One of the major aims of lattice QCD (LQCD) is to calculate electroweak decay and transition amplitudes from first principles, so as to use experimental results to test the standard model. A classic example is the K->2pi amplitude, and in particular its CP-violating part, where experimental results have long been available but which only recently has become accessible to LQCD. In this talk I describe the status of efforts to extend the methodology to processes involving three or more particles, e.g. K->3pi, one of whose aims is to eventually calculate CP violation in D decays in the standard model, so as to compare to the recent LHCb measurement. The challenges include both the development of formalism relating finite-volume correlators to infinite-volume amplitudes and the need to calculate many finite-volume energy levels with good accuracy using numerical simulations. Possible applications here include studying traditional resonances such as the omega as well as the recently discovered doubly-charmed tetraquark state.