The connection between the geometry of knot complement and Jones polynomial or related quantum invariants has been a major problem in quantum topology. The famous conjectures like the Volume conjecture and the Slope conjecture predict that the hyperbolic geometry and the topology of surfaces in knot complement are closely related to colored Jones polynomials. Here we will focus on the connection between Jones polynomial and the topology of essential knot surfaces. In this lecture after a quick overview, we will talk about the problem of fiber detection of state surfaces of a knot diagram and its relation to Jones polynomial.