Most currents around here come in tens-of-milliamps, maybe a few hundred, tops, but it’s worth noting some curves from the Tektronix AM503 current amplifier manual for A6302 Hall effect probes:

The maximum current drops from 20 A for frequencies above 20 kHz:

There’s a 100 A·μs pulse charge limit:

Because the probe is actually a pulse transformer, its internal termination imposes a (small) load on the input circuit:

The specs are 100 mΩ at 1 MHz and 500 mΩ at 50 MHz, which means the load is essentially zilch for the circuits and signals I deal with.
The Tektronix Probes for Current Measurement Systems has some useful descriptions.
Memo to Self: Should any of those limits matter, rethink what you’re doing.
An interesting story about the AM503 design from someone who lived through it.