Tabletop plasma accelerators can now produce GeV-range electron beams and femtosecond X-ray pulses, providing compact radiation sources for medicine, nuclear engineering, materials science and high-energy physics. In these accelerators, electrons surf on electric fields exceeding 100 GeV m^{−1}, which is more than 1,000 times stronger than achievable in conventional accelerators. These fields are generated within plasma structures (such as Langmuir waves or electron density ‘bubbles’) propagating near light speed behind laser or charged-particle driving pulses. Here, we demonstrate single-shot visualization of laser-wakefield accelerator structures for the first time. Our ‘snapshots’ capture the evolution of multiple wake periods, detect structure variations as laser–plasma parameters change, and resolve wavefront curvature; features never previously observed.