Dielectric laser acceleration (DLA) is a promising approach to accelerate single electrons at a high repetition rate to GeV energies, for indirect dark matter searches. Relevant concepts include the integration of the dielectric structure inside the laser oscillator. To efficiently use muons for high energy physics applications, they need to be accelerated rapidly, before they decay. Plasma acceleration achieves GV/m accelerating fields and could be ideal for accelerating to muon-collider energies. Single muons could also be accelerated in DLAs for dark matter searches. They could be injected from existing low-intensity muon sources, such as the one at PSI. A workshop organized in the frame of the EU project “Innovation Fostering in Accelerator Science and Technology” (I.FAST) focused on GHz Rate & Rapid Muon Acceleration for Particle Physics to address these topics. We report highlights and future research directions.