Aqueous sorption processes play an important role in, for example, pollutant binding to natural nanoparticles, colloid stability, separation and enrichment of components and remediation processes. In this article, which is a tribute to Hans Lyklema, models of localized (ad)sorption of molecules and ions from aqueous solution on homogeneous and heterogeneous nanoparticles are presented. The discussed models range from ideal monocomponent sorption on homogeneous (Langmuir) and heterogeneous sites, to multicomponent ideal sorption on homogeneous and heterogeneous sites, multicomponent multisite ion complexation with charge distribution (CD-MUSIC) and non-ideal competitive adsorption on heterogeneous sites (NICA). Attention is also paid to lateral interaction, site-induced aggregation, binding stoichiometry and multilayer formation. Electrical double layer models are discussed in relation to ion binding on impermeable and permeable nanoparticles. Insight in models that can describe sorption of molecules and ions on nanoparticles leads to awareness of the limitations of using simple models for complex systems and is needed for the selection and application of an appropriate model for a given system. This is relevant for all practical sorption processes and for a better understanding of the role of natural nanoparticles in the binding of nutrients and pollutants.