I will discuss results showing that every homologically trivial curve in a closed hyperbolic 3-manifold M bounds an essential surface and that every homology class in the second rational homology of M contains a quasifuchsian representative. Other results include the estimate on the growth of torsion in the homology of finite covers of M and some application of the surface subgroup method in geometric group theory (for example to the study of Cannon's Conjecture and related problems). Most of this is ongoing work and different parts it involve various collaborators (Agol, Kahn, Liu, etc.).