  We use a custom shear cell coupled to an optical microscope to investigate at
the particle level the yielding transition in concentrated emulsions subjected
to an oscillatory shear deformation. By performing experiments lasting
thousands of cycles on samples at several volume fractions and for a variety of
applied strain amplitudes, we obtain a comprehensive, microscopic picture of
the yielding transition. We find that irreversible particle motion sharply
increases beyond a volume-fraction dependent critical strain, which is found to
be in close agreement with the strain beyond which the stress-strain relation
probed in rheology experiments significantly departs from linearity. The
shear-induced dynamics are very heterogenous: quiescent particles coexist with
two distinct populations of mobile and `supermobile' particles. Dynamic
activity exhibits spatial and temporal correlations, with rearrangements events
organized in bursts of motion affecting localized regions of the sample.
Analogies with other sheared soft materials and with recent work on the
transition to irreversibility in sheared complex fluids are briefly discussed.
