Historical laws as limiting cases of the ideal gas law
Boyle's law (P inversely proportional to V at constant T and n) emerges from the ideal gas law PV = nRT by holding T and n fixed. Charles's law (V proportional to T at constant P and n) follows by holding P and n fixed. Gay-Lussac's law (P proportional to T at constant V and n) holds volume and mole count constant. Avogadro's law (V proportional to n at constant P and T) was discovered empirically before the ideal gas law: equal volumes of different gases at the same temperature and pressure contain the same number of molecules. Each of these special cases was discovered experimentally over the 1600s-1800s by changing one variable while holding others fixed. The ideal gas law unifies them: PV = nRT says that the product PV is proportional to the total number of particles and the absolute temperature, regardless of which variables you manipulate.
Deviations at high pressure and low temperature
Real gases deviate from the ideal law at high pressure (molecules are close enough to repel each other) and low temperature (attractive forces between molecules become significant). The van der Waals equation corrects for these effects with two parameters: a accounts for intermolecular attractions, and b accounts for molecular volume. Near standard temperature and pressure, most gases behave ideally enough for engineering calculations. But near a phase transition (liquid forming from gas), or at extreme pressures (deep in planetary cores), the ideal assumption breaks down completely. Quantum gases (helium below 2 K, ultracold atoms) show additional phenomena like Bose-Einstein condensation where the ideal law is useless.