Multi-object spectroscopy has been a key technique contributing to the current era of precision cosmology. From the first exploratory surveys of the large-scale structure and evolution of the universe to the current generation of superbly detailed maps spanning a wide range of redshifts, multi-object spectroscopy has been a fundamentally important tool for mapping the rich structure of the cosmic web and extracting cosmological information of increasing variety and precision. This will continue to be true for the foreseeable future, as we seek to map the evolving geometry and structure of the universe over the full extent of cosmic history in order to obtain the most precise and comprehensive measurements of cosmological parameters. Here I briefly summarize the contributions that multi-object spectroscopy has made to cosmology so far, then review the major surveys and instruments currently in play and their prospects for pushing back the cosmological frontier. Finally, I examine some of the next generation of instruments and surveys to explore how the field will develop in coming years, with a particular focus on specialised multi-object spectrographs for cosmology and the capabilities of multi-object spectrographs on the new generation of extremely large telescopes.