Additional to the classic current transformer method, there are now available devices which look like current transformers in that they generally have a toroid form that you pass the current wire through, (optionally with more than 1 turn), but are Hall-effect sensors. Some simply amplify the sample, other more accurate types use a null coil and a feedback method in the internal electronics.
Small ferrite current transformers can also do an excellent job. They just have to have a core big enough not to saturate. Ferrites have such a high permeability, they could more easily saturate unless provided with an intentional air gap.
Hall-effect devices can work down to DC. Either sort can measure complex phase components that may be present . Choose those with bandwidths high enough to to faithfully sample the pulse-width modulated pseudo-AC used to drive AC motors from inverters and servo drives.