Perhaps the best use:
Feed the input of an amp (complete or one-stage) to 'scope H-input, feed the amp output to 'scope V-input.
Apply variable signal.
If the amp is "perfect" (constant gain at any input level), you get a slanted straight line.
No amp is perfect to infinite signal. And the way it gives-up at high signal is the way we add emphasis to the thin sound of a naked steel string.
It is too muggy tonight to mock-up a "typical" amplifier. I pulled out a perfect amplifier and tangled its output with silicon diodes (I have a good sense of where they get bent).
FWIW: some milder fuzz-boxes are fairly similar to this plan.

The "perfect" amp has gain of 10. If we measure its output (red line), it is always exactly 10 times the input, at any input (in this plot, up to 0.3V in 3V out).
Real amplifiers (green line) won't make infinite output, and are never perfectly straight lines.
0.1V input does make
almost 1V output. But 0.2v in makes +1.4V and -1.5V. 0.3V in makes +1.7V and -2V. 0.5V in, +1.8V and 2.4V. And, not shown, 5V in gives +2.3V -3V.
The output never rises past about 2 or 3 volts. And not symmetric + and -. Good to know.
If you had say a 6V6 and it needed +/-17V at the grid to smack the whole 4.8 Watts of output, this circuit won't do it.
Another tidbit you need to know: it is hard to see in this graph, but the left-right trace does not lay exactly on the right-left trace. This is phase shift. If you measure a tone control, or any circuit with limited frequency response (almost any gitar amp circuit), that ideal straight line opens up into an oval.
Another thing: you don't have to adjust the scope when you change frequency. In fact you can see nonlinearity with any signal, even if you don't know what it "should" look like. You can watch signals as you play guitar.