We consider a cellular massive MIMO system where swarms of wireless repeaters are deployed to improve coverage. These repeaters are full-duplex relays with small form factors that receive and instantaneously retransmit signals. They can be deployed in a plug-and-play manner at low cost, while being transparent to the network--conceptually they are active channel scatterers with amplification capabilities. Two fundamental questions need to be addressed in repeater deployments: (I) How can we prevent destructive effects of positive feedback caused by inter-repeater interaction (i.e., each repeater receives and amplifies signals from others)? (ii) How much performance improvement can be achieved given that repeaters also inject noise and may introduce more interference? To answer these questions, we first derive a generalized Nyquist stability criterion for the repeater swarm system, and provide an easy-to-check stability condition. Then, we study the uplink performance and develop an efficient iterative algorithm that jointly optimizes the repeater gains, user transmit powers, and receive combining weights to maximize the weighted sum rate while ensuring system stability. Numerical results corroborate our theoretical findings and show that the repeaters can significantly improve the system performance, both in sub-6 GHz and millimeter-wave bands. The results also warrant careful deployment to fully realize the benefits of repeaters, for example, by ensuring a high probability of line-of-sight links between repeaters and the base station.