This tutorial review covers recent developments in catalytic carbocyclisation of functionalised alkynes with external nucleophiles catalysed by gold, platinum and other electrophilic metals. Substrates of such reactions require a tethered functionality to react with the alkyne to complete a carbocyclic ring. We classify the reactions according to the tethered functionalities to illustrate the diversity of the carbocyclisations; these substrates include: (1) alkyne-alkyne, (2) alkyne-allene, (3) alkyne-alkene, (4) oxo-alkynes and (5) oxo-diynes and triynes. Besides their mechanistic interest, these reactions meet atom economy criteria because complex and functionalised carbocyclic products are easily assembled in a cascade sequence from readily available alkynes and nucleophiles.