Context. The outer regions of planetary systems host dusty debris discs analogous to the Kuiper belt (exoKuiper belts), which provide crucial constraints on planet formation and evolution processes. ALMA dust observations have revealed a great diversity in terms of radii, widths, and scale heights. At the same time, ALMA has also shown that some belts contain CO gas, whose origin and implications are still highly uncertain. Most of this progress, however, has been limited by low angular resolution observations that hinder our ability to test existing models and theories. Aims. High-resolution observations of these belts are crucial for understanding the detailed distribution of solids and for constraining the gas distribution and kinematics. Methods. We conducted the first ALMA large programme dedicated to debris discs: the ALMA survey to Resolve exoKuiper belt Substructures (ARKS). We selected the 24 most promising belts to best address our main objectives: analysing the detailed radial and vertical structure, and characterising the gas content. The data were reduced and corrected to account for several systematic effects, and then imaged. Using parametric and non-parametric models, we constrained the radial and vertical distribution of dust, as well as the presence of asymmetries. For a subset of six belts with CO gas, we constrained the gas distribution and kinematics. To interpret these observations, we used a wide range of dynamical models. Results. The first results of ARKS are presented as a series of ten papers. We discovered that up to 33% of our sample exhibits substructures in the form of multiple dusty rings that may have been inherited from their protoplanetary discs. For highly inclined belts, we found that non-Gaussian vertical distributions are common and could be indicative of multiple dynamical populations. Half of the derived scale heights are small enough to be consistent with self-stirring in low-mass belts (Mbelt ≤ MNeptune). We also found that 10 of the 24 belts present asymmetries in the form of density enhancements, eccentricities, or warps. We find that the CO gas is radially broader than the dust, but this could be an effect of optical depth. At least one system shows non-Keplerian kinematics due to strong pressure gradients, which may have triggered a vortex that trapped dust in an arc. Finally, we find evidence that the micron-sized grains may be affected by gas drag in gas-rich systems, pushing the small grains to wider orbits than the large grains. Conclusions. ARKS has revealed a great diversity of radial and vertical structures in exoKuiper belts that may arise when they are formed in protoplanetary discs or subsequently via interactions with planets and/or gas. We encourage the community to explore the reduced data and data products that we have made public through a dedicated website.