Graph manifolds are usually considered as a simple class of 3-manifolds. However many open questions are unsolved till recently. We will discuss the following problems.

• Are the covering degrees uniquely determined by the manifolds involved?
• Is every graph manifold with non-empty boundary finitely covered by a surface bundle over the circle?
• Can each least area $\pi_1$-injective surface in graph manifold be lifted to an embedded surface in a finite cover?
• Is the "simple loop conjecture" true for graph manifolds?