For higher powered DC loads, there are Hall effect sensors. These usually come as plastic-enclosed devices with a hole in them, through which you route one of the high-current wires. They need some DC power, usually 5V or so, and you get a voltage out proportional to the current. They sense the magnetic field from the wire, without requiring a direct connection, which is good when you're measuring high current, high voltage, or both. Some have a split ring so you can install the sensor around an existing wire without cutting it.

For AC, there are current transformers, which install the same way, and put out a small current in a fixed ratio to the current in the wire being sensed.

The hand-held version is a clamp-around AC/DC current meter, a common tool.

These are all standard, modestly priced items.