Soft robotics is attractive for wearable applications that require conformal interactions with the human body. Soft wearable robotic garments hold promise for supplying dynamic compression or massage therapies, such as are applied for disorders affecting lymphatic and blood circulation. In this paper, we present a wearable robot capable of supplying dynamic compression and massage therapy via peristaltic motion of finger-sized soft, fluidic actuators. We show that this peristaltic wearable robot can supply dynamic compression pressures exceeding 22 kPa at frequencies of 14 Hz or more, meeting requirements for compression and massage therapy. A large variety of software-programmable compression wave patterns can be generated by varying frequency, amplitude, phase delay, and duration parameters. We first demonstrate the utility of this peristaltic wearable robot for compression therapy, showing fluid transport in a laboratory model of the upper limb. We theoretically and empirically identify driving regimes that optimize fluid transport. We second demonstrate the utility of this garment for dynamic massage therapy. These findings show the potential of such a wearable robot for the treatment of several health disorders associated with lymphatic and blood circulation, such as lymphedema and blood clots.