DUNE will be the world's largest neutrino experiment due to take data in 2025. Here are described the data acquisition (DAQ) systems for both of its prototypes, ProtoDUNE single-phase (SP) and ProtoDUNE dual-phase (DP) - due to take data later this year. ProtoDUNE also breaks records as the largest beam test experiment yet constructed, and are the fundamental elements of CERN's Neutrino Platform. This renders each ProtoDUNE an experiment in its own right and the design and construction have been chosen to meet this scale. Due to the aggressive timescale, off-the-shelf electronics have been chosen to meet the demands of the experiments where possible. The ProtoDUNE-SP cryostat comprises two primary subdetectors - a single phase liquid Argon TPC and a companion Photon Detector. The TPC has two candidate readout solutions under test in ProtoDUNE-SP - RCE (ATCA-based) and FELIX (PCIe-based). Fermilab's artDAQ is used as the dataflow software for the single phase experiment. ProtoDUNE-DP will readout out the dual-phase liquid argon detector using a microTCA readout solution. Timing and trigger electronics and software are also described. Compression and triggering will take ~480 Gb/s (SP); ~130 Gb/s (DP) of data from the front-end and reduce it sufficiently to 20 Gb/s (each) bandwidth to permanent data storage in CERN's EOS infrastructure. This paper describes the design and implementation of the TDAQ systems as well as first measurements of their performance.