Neutrino tridents are rare Standard Model (SM) processes involving the creation of a charged-lepton pair via an energetic neutrino scattering with a nucleus. These processes provide a precision test of the SM weak sector, and can also serve as a sensitive probe of beyond-the-SM physics. We will present a detailed study of the SM neutrino tridents, including (i) a full 2→4 analytic calculation of the cross section, (ii) both coherent and incoherent scatterings, and (iii) the nuclear modeling uncertainties, in a systematic way. Finally, we comment on the detection prospects of trident events at future accelerator neutrino facilities, such as DUNE.