Multivalency is a powerful concept which explains the strong binding observed in biological systems and guides the design and synthesis of ligands for self-assembly and molecular recognition in Chemistry. The phenol-formaldehyde cyclic oligomers, called calixarenes, have been used as scaffolds for the synthesis of multivalent ligands thanks to the fact that they have a variable number of reactive positions for attaching the ligating functions, well defined conformational properties and, in some cases, cavities of molecular dimensions eventually able to encapsulate guest species. This tutorial review illustrates the fundamental aspects of multivalency and the properties of calixarene-based multivalent ligands in lectin binding and inhibition, DNA condensation and cell transfection, protein surface recognition, self-assembly, crystal engineering, and nanofabrication.