Many materials around us respond elastically to small applied stresses, but flow oncea threshold stress (the yield stress) is exceeded. This is the case for food products,powders, cosmetics, foams, etc… It turns out that understanding the yield stresstransition in these materials, often called soft glasses, is a challengingquestion. Similar to structural glasses, soft glasses exhibit aging and complexdynamics. Also, the size of the elementary building block of a soft glass is usuallyranging from 1 micron to 1mm, ruling out the possibility to investigate the problemby molecular dynamics.Recently, a new approach has been proposed: using a mesoscopic formulation of thesystem, the dynamics of relative simple soft glasses, like foams or micro emulsions,has been investigated. Numerical simulations allow the computation of severalimportant properties of the systems, such as the yield stress transition. In this talk, Iwill review the new approach and explain how the complexity of soft glassdynamics may be disentangled in a systematic way.