We have measured the yield transition of monodisperse emulsions as the volume fraction, phi, and droplet radius, alpha, are varied. We study the crossover from the perturbative shear regime, which reflects the linear viscoelastic properties, to the steady shear regime, which reflects nonlinear, plastic flow. For small oscillatory strains of peak amplitude gamma, the peak stress, tau, is linearly proportional to gamma. As the strain is increased, the stress becomes nonlinear in gamma at the yield strain, gamma(y). The phi dependence of gamma(y) is independent of alpha and exhibits a minimum near the critical volume fraction, phi(c) approximate to 0.635, associated with the random close packing of monodisperse spheres. We show that the yield stress, tau(y), increases dramatically as the volume fraction increases above phi(c); tau(y) also scales with the Laplace pressure, sigma/alpha, where sigma is the interfacial tension. For comparison, we also determine the steady shear stress over a wide range of strain rates, gamma. Below phi approximate to 0.70, the flow is homogeneous throughout the sample, while for higher phi, the emulsion fractures resulting in highly inhomogeneous flow along the fracture plane. Above phi approximate to 0.58, the steady shear stress exhibits a low strain rate plateau which corresponds with the yield stress measured with the oscillatory technique. Moreover, tau(y) exhibits a robust power law dependence on gamma with exponents decreasing with phi, varying from 2/3 to 1/2. Below phi approximate to 0.58, associated with the colloidal glass transition, the plateau stress disappears entirely, suggesting that the equilibrium glassy dynamics are important in identifying the onset of the yield behavior.