Number counts of galaxy clusters are a well established cosmological probe, which infers the cosmological model by measuring the abundance of clusters as a function of their mass and cosmic age. We review first the key ingredients for cluster cosmological inference, identifying two main regions of systematic uncertainty: cluster mass measurements and cluster selection modelling. Based on recent work for the South Pole Telescope and the Dark Energy survey cluster cosmological analyses, we present how to tackle these issues via a combination of Bayesian population modelling, cosmological volume hydrodynamical simulations and multi-wavelength observations. Finally, we outline how these new methods will lead to robust cluster cosmological inference in the age of the next generations surveys like eROSITA, Rubin, Euclid, and CMB-Stage IV.