Just a very quick note:
You will want to look at the following:
current transformers (most basic, AC only)
These work just like any other transformer; current in the primary induces a magnetic field which induces current in the secondary.
hall effect current sensors (simple, will give both AC and DC)
active hall effect current sensors
These work by measuring the magnetic field produced by the current being measured. In passive hall effect devices the current causes a change in output of the sensor. In active hall effect devices a circuit acts to null the magnetic field being measured; the nulling current is the measure of the current being sensed.
rogowski coils
These measure the rate change of the magnetic field being measured, and the magnetic field is produced by the current being measured. So the output needs to be integrated to get the current, and can not be accurate for DC. But you have the benefit of not needing an iron core, so you can have a flexible measuring lead that you just wrap around the conductors being measured.
-Jon