I will report on the work in progress with S. Anjos and M. Pinsonnault concerning configuration spaces of symplectic balls in the standard complex projective plane. A few weeks ago Martin showed that when the balls are small their configuration space is homotopy equivalent to the configuration space of points. I will discuss what is happening if the balls are bigger. I will also try to put it into a more general context of configuration of rigid balls in domains of a Euclidean space.