This review summarized the developments in the field of volatile silver complexes, which can serve as precursors in gas-transport reactions for the production of thin films and metal nanoparticles via chemical vapor deposition (CVD) and atomic layer deposition (ALD). Silver-based films and nanoparticles are widely used in various high-tech fields, including medicine. For effective use in CVD and ALD processes, the properties of silver precursors must be balanced in terms of volatility, thermal stability, and reactivity. In this review, we focus on the synthesis and comprehensive analysis of structural and thermal characteristics for the most promising classes of volatile silver complexes, as well as organometallic compounds. Following the specifics of silver chemistry, some features of the use of precursors and their selection, as well as several key directions to improving the efficiency of silver material deposition processes, are also discussed.