Open-cage fullerenes can act as hosts for small molecules such as water, nitrogen, or hydrogen, forming endohedral fullerenes. Following a brief summary of carbon, nitrogen, and oxygen insertion in the fullerene framework to form homofullerenes, methods of creating a hole in the fullerene surface are surveyed. Techniques of hole enlargement and the insertion of atoms or molecules through the orifice to form endohedral fullerenes are described. Finally, the possibility of subsequent closure of the hole is considered.