The simple loop conjecture for 3-manifolds states that every 2-sided immersion of a closed surface into a 3-manifold is either injective on fundamental groups or admits a compression. This can be viewed as a generalization of the Loop Theorem to immersed surfaces. We will give a brief history of this problem and outline a solution when the target 3-manifold is a torus bundle over a circle or a torus semi-bundle.