At a basic level, algebraic topology is the study of topological spaces by means of algebraic invariants. The key word here is "topological spaces". (Basic) algebraic topology is very useful in other areas of mathematics, especially, in geometry(I would say almost in all geometry).

I'm not an algebraic topologist myself, so I know only basic techniques. However, I'm intrigued by modern tool in homotopy theory. For example, we have simplicial homotopy theory, where one studies simplicial sets instead of topological spaces.

As far as I understand, simplicial techniques are indispensible in modern topology. Then we have axiomatic model-theoretic homotopy theory, stable homotopy theory, chromatic homotopy theory. Recently, we got a topological version of algebraic geometry, namely spectral algebraic geometry which is proved useful in studying topological modular forms.

But one may wonder what is it for? Those are really fancy and sometimes beautiful tools, but what are exactly the questions modern algebraic topology seeks to answer? Because It feels it's really not part of topology anymore, it's more as topology now is a small part of algebraic topology/homotopy theory.

So, I would like to hear about goals and perspectives of modern homotopy theory from those working on it. I hope this question might be useful to someone else.