The key to explaining and controlling a range of quantum phenomena is to study how information propagates around many-body systems. Quantum dynamics can be described by particle-like carriers of information that emerge in the collective behaviour of the underlying system, the so-called quasiparticles(1). These elementary excitations are predicted to distribute quantum information in a fashion determined by the system's interactions(2). Here we report quasiparticle dynamics observed in a quantum many-body system of trapped atomic ions(3,4). First, we observe the entanglement distributed by quasiparticles as they trace out light-cone-like wavefronts(5-11). Second, using the ability to tune the interaction range in our system, we observe information propagation in an experimental regime where the effective-light-cone picture does not apply(7,12). Our results will enable experimental studies of a range of quantum phenomena, including transport(13,14), thermalization(15), localization(16) and entanglement growth(17), and represent a first step towards a newquantum-optic regime of engineered quasiparticles with tunable nonlinear interactions.