Nondestructive evaluation (NDE) is the inspection of samples for corrosion and physical defects without altering them in any way. NDE has a critical role in the robotic inspection of energy pipelines in order to prevent catastrophic failures. Magnetic flux leakage (MFL) sensing is by far the most effective technique for robotic inspection of ferromagnetic pipes and tubular specimens. Defect detection using MFL sensing is a mature area of work, but defect characterization using MFL sensing is an open research problem. Several issues involved in this process are not well understood---for example, the interplay of the components of the 3-dimensional MFL field for 3-dimensional defects, the spatial properties of the MFL field components, the effect of sensor lift-off on MFL signals, and the relationships between defect properties and MFL signal properties. This dissertation addresses these issues using a systematic approach. First the MFL sensing problem is decomposed into the forward and inverse problems. Subsequently, a tractable forward model is presented which is capable of predicting the 3-dimensional MFL field of a known 3-dimensional surface-breaking defect. Important properties of the MFL field and their correlation with sensing parameters and defect parameters are established using the model and simulation. A linear inversion technique is presented which exploits the structure and properties of the forward model to characterize defects based on measured MFL signals. This dissertation also proposes a general framework to solve the inverse problem independent of the NDE modality in use. This framework uses the principles of data fusion and neural networks, and is illustrated using both MFL signals as well as another NDE technique, namely ultrasonic testing. Finally, this dissertation addresses the problem of pipe wall thickness measurement as a special case of the inverse problem and develops a novel technique for pipe wall thickness measurement using MFL signals.