Carbon nanotubes are promising materials for various applications. In recent years, progress in manufacturing and functionalizing carbon nanotubes has been made to achieve the control of bulk and surface properties including the wettability, acid-base properties, adsorption, electric conductivity and capacitance. In order to gain the optimal benefit of carbon nanotubes, comprehensive understanding on manufacturing and functionalizing carbon nanotubes ought to be systematically developed. This review summarizes methodologies of manufacturing carbon nanotubes via arc discharge, laser ablation and chemical vapor deposition and functionalizing carbon nanotubes through surface oxidation and activation, doping of heteroatoms, halogenation, sulfonation, grafting, polymer coating, noncovalent functionalization and nanoparticle attachment. The characterization techniques detecting the bulk nature and surface properties as well as the effects of various functionalization approaches on modifying the surface properties for specific applications in catalysis including heterogeneous catalysis, photocatalysis, photoelectrocatalysis and electrocatalysis are highlighted.