Brazing is a critical materials-joining technology because it can join like or dissimilar materials, create high performance joints for use at high operating temperatures, and create thousands of joints simultaneously due to how the liquid brazing filler metal wets the base material and flows. The latter aspect enables the creation of high operating-temperature topologically-complex brazed structures, like plate-fin heat exchangers, from low-cost stamped sheet steel which would be impossible to produce by traditional manufacturing techniques—except for metal 3D printing which is extremely slow and expensive. Specifically, stainless steel heat-exchangers brazed with Ni-based amorphous brazing foils play a crucial role in energy conservation and pollution control systems. While the primary purpose of some brazed joints is simply to create a hermetic seal, most braze joints are expected to carry substantial structural loads. Thus, robust methods for measuring braze strength and interpreting these data are essential to the advancement of the field of structural brazing.Currently, the overwhelming majority of researchers who investigate the strength of brazed joints utilize two equally inadequate paths. The first path involves characterizing braze microstructure using traditional techniques (SEM/EDX, indentation) before making overly-broad purely-qualitative statements about how the microstructure is expected to impact braze strength. This path has minimal explanatory power because there is no indication as to the magnitude of each effect. The second path involves the use of macroscale mechanical tests of brazed joints and reporting average braze failure stresses with the intention of determining braze bulk material properties such as ultimate shear and tensile strengths. This path also has minimal explanatory power because the stresses in brazed joints are rarely if ever uniformly distributed across the braze (The stress states of the most common braze strength samples are reviewed in the Background section of this dissertation—as a concise review of this material does not exist in the open literature). This current statis quo is clearly unacceptable. In this work, we combine micromechanics, continuum mechanics, and materials science to create a concise comprehensive model to measure and interpret the strength of brazed single-lap joints. The brazed single-lap joint is chosen as it is the most commonly used sample to measure brazed strength, largely because it is representative of common braze joints and simple/inexpensive to execute. We develop a three-point model based on how the sample geometry dictates the continuum stress state, the base metal properties control the stress state’s evolution with increasing applied stress, and the braze microstructure controls local failure. Substantial effort is devoted to qualitatively and quantitively describing the stress state’s dependence on both overlap ratio and applied stress. We find that a wide variety of phenomena that have not previously been explained can now be explained when each of our three points are considered simultaneously.