Well, technically, both newtonian physics, relativity and QM work in tandem, all the time. However, some of the abstractions break down - for example, when you're dealing with an electron in isolation, it behaves well in accord with newtonian physics. The same way, even if that electron moves at half the speed of light, from the POV of the electron, it sill behaves classically. The interactions are the interesting part, and that's where the perceived "limits" lie.
Now, even you, as a macroscopic object, are subject to quantum physics. However, the classical approximation is by far close enough to the reality, that adding QM to the equation doesn't really change much. Think about it just like with e.g. the EM charge of an atom - no atom is truly neutral. It's just that the tiny electro-magnetic is easily lost in the tons of other interactions the atom and its constituent parts undergo - in this case, simple thermal effects are much stronger in magnitude than the moment.
One interesting "limit" for QM I've read about can be summarized as this: quantum mechanical effects are important when the physical delimitation of the "particle" is significantly bigger than the wave-length of that "particle". So for example, individual electrons will tend to behave less classically in EM interactions, because most of the EM charge of the electron is concentrated in a radius significantly smaller than the wave-length of the electron. On the other hand, your body is much larger than the wave-length of your body as a whole, so you as a whole tend to behave rather classically, even though your constituent parts don't. Taking a CPU as an example, every single transistor is dependent on quantum physics (quantum tunelling in particular) to work, but the processor as a whole does not display non-classical behaviour - in fact, even the transistor itself, as a black box, does not behave "quantumly".
Of course, all of this depends on accepting the quantum reality to be the more fundamental, or "closer to the territory" than newtonian physics. This may or may not be so, and there's a lot of debate on the specifics, as well as the major points (see the various interpretations of quantum physics, for example).
(Disclaimer: I am not an expert on the subject, and I don't have any special education in quantum physics.)