Plasma-based accelerators use the strong electromagnetic fields that can be supported by plasmas to accelerate charged particles to high energies. Accelerating field structures in plasma can be generated by powerful laser pulses or charged particle beams. This research field has recently transitioned from involving a few small-scale efforts to the development of national and international networks of scientists supported by substantial investment in large-scale research infrastructure. In this New Journal of Physics 2020 Plasma Accelerator Roadmap, perspectives from experts in this field provide a summary overview of the field and insights into the research needs and developments for an international audience of scientists, including graduate students and researchers entering the field.