  We consider two minimal models of active fluid droplets that exhibit complex
dynamics including steady motion, deformation, rotation and oscillating motion.
First we consider a droplet with a concentration of active contractile matter
adsorbed to its boundary. We analytically predict activity driven instabilities
in the concentration profile, and compare them to the dynamics we find from
simulations. Secondly, we consider a droplet of active polar fluid of constant
concentration. In this system we predict, motion and deformation of the
droplets in certain activity ranges due to instabilities in the polarisation
field. Both these systems show spontaneous transitions to motility and
deformation which resemble dynamics of the cell cytoskeleton in animal cells.
