The weak intermolecular interactions have attracted considerable interest in recent years owing to their crucial role in different research areas such as supramolecular chemistry, crystal engineering and modern biological science. Here it is illustrated how computational chemistry hand-in-hand with experimental outcomes can assist in describing weak non-covalent interactions, and more specifically, homopolar dihydrogen interactions. Selected state-of-the-art computational approaches are conjunctly exercised in a tutorial-style manner to evaluate existence, nature and energetics of some O/C—H···H—C homopolar dihydrogen interactions. Satisfactory results, both in terms of accuracy and computational cost, were obtained. Readers with a general interest in computational non-covalent chemistry – from relative beginners to experts – will gain a lot from thinking through the different analyses and case study examples covered in this contribution.