relation between current,voltage and resistance

i want to know the relation between voltage,current & resistance , apart from this ohm's law V=IR.Because in zener diodes,current does not increase accordingly with the voltage.At BREAKDOWN POINT, voltage remains the same as the current increases manifold.And in several other cases,even if there is a low voltage,there exists a high current flow.How are they possible!!!

The resistivity of any material is related to the mobility of the charge carriers within it by:

$$\rho = \frac{1}{ne\mu}$$

where $\mu$ is the mobility, $e$ is the electronic charge and $n$ is the number density of charge carriers. I've deliberately used the term charge carriers rather than electrons because in semiconductors like diodes the carriers can be holes as well as electrons.

Obviously the electron charge $e$ is a constant, so changes in the resistance arise either from changes in the mobility or the carrier density. In a metal neither of these change with applied voltage, so in a metal the resistance is independant of voltage.

By contrast in a reversed biased diode the carrier density is not constant. As you increase the voltage you increase the energy of the electrons flowing across the depletion layer. At some point the energy gets high enough to excite bound electrons into the conduction band and we get an avalanche beakdown. The carrier density rises rapidly and hence the resistivity falls rapidly, so in a diode the resistance is strongly dependant on voltage.

This argument applies to any material. If you see a resistance that varies with voltage, temperature or whatever else, this will be due to changes in the carrier mobility and/or density.

I'm not sure what you are asking, but I'll address one point.

Ohm's Law, like many other physical laws, is an idealization. It applies only to ideal systems, and ideal systems do not exist. But Ohm's Law is useful because it accurately describes a very large class of real systems. Even for systems within this class it is only an approximation. One will find very slight deviations from Ohm's Law if one looks carefully enough with very accurate, precise equipment. And for any system, eventually some breakdown voltage will be reached beyond which Ohm's Law obviously fails to apply.

As you point out, there are many materials for which Ohm's Law simply does not apply.