In this video, we present a numerical study on the dynamics of a composite fluid particle in flow. Examples of such composite fluid particles include nucleated cells, double emulsions and cell-encapsulating droplets. We consider a finite-size spherical particle encapsulated in a deforming droplet under creeping shear flow and investigate whether this composite system will stay concentric or not. Despite the simple situation, we have explored several eccentric equilibrium solutions where the system exhibits spontaneous symmetry breaking and unsteady dynamics emerging through supercritical pitchfork and Hopf bifurcations; the particle can execute spanwise migratory and/or in-plane orbital motions. These bifurcations are attributed to the hydrodynamic particle-droplet interactions. More details are referred to our article, 'Bifurcation Dynamics of a Particle-Encapsulating Droplet in Shear Flow' in Phys. Rev. Lett, 119 (6), 2017.