Wait, wait, wait - we might be just using the word differently, but I would definitely not say that Newtonian mechanics is no longer "relevant". Sure, there are

Wait, wait, wait - we might be just using the word differently, but I would definitely not say that Newtonian mechanics is no longer "relevant". Sure, there are more accurate theories - even in the absence of gravitational fields, and at scales where you can ignore any quantum effects, special relativity is more correct, in the sense that Newtonian mechanics will give you misleading results at very high velocities. But that doesn't mean it's not longer relevant. Suppose you want to model a fluid mechanics problem where the speeds are all well below the speed of light (so any fluids problem outside of a few astrophysics scenarios). You will be able to get far further using Newtonian mechanics, and derive far more results, because of the relative simplicity of Newtonian mechanics. Trying to derive everything using special relativity would get very messy, and would impede your understanding of what matters at slow speeds.