We study oil in water emulsions when the interaction between the droplets becomes strongly adhesive, causing them to stick together. However, the droplets still retain their integrity and do not coalesce. By using emulsions with droplets that are monodisperse in size, we are able to clearly observe their structure when the emulsions become adhesive. We show that the structure of strongly adhesive emulsions reflects a complex interplay among the strength of the adhesion, the droplet volume fraction, phi, and the time evolution of the adhesion. Initially, strong adhesion of the droplets leads to the formation of an emulsion gel. Moreover, the gel possesses a well-defined characteristic length scale, d(c), as evidenced by an intense ring of small angle light scattering. The characteristic length scale decreases as the droplet volume fraction increases. At low phi, the structure of the emulsion gel is fractal on length scales shorter than d(c), and the measured fractal dimension suggests that the gelation mechanism is controlled by diffusion-limited cluster aggregation. However, at higher phi, the short range structure is more compact, rather than fractal, and a different mechanism must be responsible for the gelation. If the strength of the adhesion is increased still further, the droplets become more deformed, resulting in massive restructuring of the emulsion gel. The structure fractures into independent, more compact flocs, eliminating the overall rigidity of the emulsion gel. These results help rationalize some of the diverse structures that are observed upon flocculation of the more usually studied polydisperse emulsions.