Nondestructive evaluation (NDE) is the inspection of samples for physical defects without altering the sample in question in any aspect. Magnetic Flux Leakage (MFL) has become one of the most widely used NDE techniques in robotic inspection of energy pipelines to prevent catastrophic failures. The MFL technique uses a magnetic field to magnetize ferromagnetic materials and correlates anomalies in the uniform field level to defects in the structure. Defect detection using the MFL technique is a mature area of work. However, defect characterization is an open research problem that can be decomposed into the Forward and Inverse Problems. The first problem deals with the characterization of the MFL signal for known defect shapes and dimensions, while the second one deals with the characterization of the defect shape from a known MFL signal. Several aspects of the MFL technique are not well understood yet, like the interplay of the MFL field for 3-dimensional defects. Another aspect that is not clear yet is the spatial properties of the MFL field components produced by complex 3-dimensional defect shapes. This dissertation addresses three issues identified with the MFL Forward Problem. An analytical 3-dimensional MFL model based on the Magnetic Dipole Model (MDM) and derived from Maxwell’s equations is presented. Under specific conditions, the magnetic field generated by a surface-breaking defect can be mathematically described as if it is caused by magnetic charges on the surface of the defect; such phenomenon can be described through Maxwell’s equations. The improved MDM characterizes the magnetic charges on the surface of the defect by using two parameters instead of one. Consequently, the MFL Forward Problem of complex defect shapes can be solved through the application of the improved model. Likewise, this thesis also studies the nature of the MFL signals in order to have a deep understanding of the Forward Problem. Therefore, a study of the correlation between the MFL signals (axial, radial, and tangential) through the improved MDM is addressed. The analysis exhibits the existence of a correlation between the three components of the MFL signal under some conditions. These results open more avenues in the field to better understand the physics of the MFL phenomenon. Hence, a methodology for the approximation of the behaviors of two MFL signal components from one extracted component is addressed. Additionally, another important approach to the MFL Forward Problem is conducted through experimentation. This dissertation explores a revolutionary 2-D type of sensing technology for application to MFL inspection known as Magneto Optical (MO) film. The feasibility of using the MO sensing in the MFL technique is presented through the development of an analytical model. Experimental and simulation validations are presented for the three approaches related to the MFL Forward Problem. Finally, this dissertation discusses the impact that these different contributions make toward solving the Inverse Problem.