In this talk, I will discuss the combinatorial aspects of graded embedding problems for Lie (super)algebras. Dynkin started the study in the 1950s in one of his seminal papers for finite-dimensional semisimple Lie algebras and it has expanded significantly since the late nineties through the work of several authors for affine and symmetrizable Kac–Moody algebras. I will present our results where we unify all the above-mentioned works systematically and prove that any root-generated subalgebra is of Kac–Moody type, essentially understanding the graded embeddings combinatorially. However, similar questions for superalgebras remain largely enigmatic – even in the finite-dimensional case. I will also discuss our recent contributions for Kac–Moody superalgebras, along with the challenges and novelties of the super case. This work is joint with Deniz Kus and Chaithra Pilakkat.