The mass flows and energy cycles within the inner regions of galaxies exert a powerful influence on the evolution of the galaxy population. The centre of the Milky Way is the only galactic nucleus for which it is possible to resolve the physical mechanisms that drive these cycles, namely star formation and feedback, while also tracing global ($\gtrsim$100 pc) processes which determine where and when star formation and feedback occur. We present an overview of ACES, the ‘Atacama Large Millimeter/submillimeter Array (ALMA) CMZ Exploration Survey’, a $\sim 1.5,\rm arcsec$ angular resolution, $0.2{\text{-}}3$ km s$^{-1}$ spectral resolution ALMA Band 3 ($85{\text{-}}102$ GHz), survey of the ‘Central Molecular Zone’ (CMZ) – the inner-100 pc of the Galaxy (l = 359.4$^\circ$ to 0.8$^\circ$). ACES spectral set-up is tuned to observe optimal tracers of the physical, chemical, and kinematic conditions in over 70 spectral features (e.g. HCO$^+$, HNCO, SiO, H40 $\alpha$, complex molecules) of the gas in the CMZ, to derive the properties of all potentially star-forming Galactic Centre gas, from global scales (100 pc) to dense $\sim$0.05 pc structures that are expected to host individual star-forming cores, down to subsonic (<0.4 km s$^{-1}$) velocity resolution. In this overview paper, we provide the scientific justification for the ACES survey, explain the choice of observational set-up, and describe the data legacy products. Finally, we show some of the initial ACES data which highlight the power of ACES’ combination of high angular resolution, unprecedented spatial dynamic range, sensitivity, spectral resolution and spectral bandwidth as an illustration of how ACES aims to understand how global processes set the location, intensity, and time-scales for star formation and feedback in the CMZ.