In this talk I will survey some results/techniques related to explicit coverings of $F_q(X)$ with prescribed ramification. Almost all results that I will discuss are related to subgroups of $GL(d,q^n)$. The constructions give us explicit equations, and the proofs use various recognition theorems from group theory. Some of the results (joint work with Abhyankar) can also be interpreted in terms of Galois groups attached to $f$-division points of various Drinfeld modules. In addition, I will also discuss some questions related to finite regular coverings with prescribed ramification.