[jacquesm]

It's at best a leaky abstraction but for some domains it is very useful. Antennas are 'magic' from the point of view of Ohms law and so on but once you move to the electromagnetic domain you will find equivalents for most of the elements in the original abstraction: impedance, reactance and so on.

[SAI_Peregrinus]

Yep, and even common nonlinear elements like diodes and transistors are non-Ohmic.

[jacquesm]

No, they are just non-linear: as the voltage goes up the current goes up in jumps because the resistance changes in a non-linear way, but it is still resistance and you can still express the system at any point of the curve using Ohm's laws and you can still compute the power lost in any part of that system using the simplest equations. A coil or a capacitor (or even a piece of wire, but there the effects are very small) are components that do not follow Ohm's laws, you need to add more parameters than just current, voltage and resistance to work out what's happening.

Tricky stuff!