The continued dominance of copper in microelectronic manufacturing is due in part to the techniques that have kept pace with the relentless trend towards smaller feature sizes. Pure and defect-free copper features can be created at these and smaller scales using gas phase deposition methods such as chemical vapor deposition (CVD) and atomic layer deposition (ALD). Here we review the deposition processes and in particular surface chemistry for depositing copper metal by CVD and ALD. A summary of known processes is given, and new trends in copper film deposition research are discussed. As well, process parameters and properties of copper films deposited from precursors using key ligand systems such as aminoalkoxides, amidinates, guanidinates, betadiketonates and betaketoiminates are presented. Surface chemistry is examined from the point of view of the similarities of CVD and ALD, considering precursors that can be used in both types of processes. This serves to highlight trends in decomposition mechanisms and illuminates some interesting similarities in process temperature and other parameters.