I often see people saying "Ohm's law doesn't apply here", usually in relation to AC circuits and diodes. They describe certain situations as being "non-Ohmic". My understanding of Ohm's law is that it always applies all the time, only it's sometimes not useful to think about it that way.
I'm the kind of person that needs to understand from the most "technically-correct" point and work upwards from there. For instance, AC isn't some special form of electricity, it's just DC with a frequently-inverted voltage. For practical engineering in the real world, it's useful to treat the two as unique, but technically speaking, it's all just electricity.
So with that in mind, does Ohm's law always apply in all situations so long as you sample an infinitely narrow point in time?
Note: When I talk about Ohm's law, I'm talking about the relationship between voltage, resistance and current: given any two you can calculate the third. I've seen some people try to describe Ohm's law as defining that a linear increase in voltage would result in a linear increase in current (which might not be true because increasing current may generate heat and also increase resistance, for instance).