Geometric finiteness is a nice property for an n-dimensional hyperbolic manifold, and one way to determine the geometric finiteness is to describe the limit set which consists of conical limit points and parabolic fixed points. On the other hand, the limit sets of geometrically infinite Kleinian groups contain infinitely many nonconical limit points. One can ask questions relating the measure-theoretic size of the limit set, conical limit set or non-conical limit set to the geometric finiteness. In this talk, we will review some existing results and conjectures about Kleinian groups with small Hausdorff dimension, and small critical exponents.