In 2013 the IceCube neutrino observatory, a cubic-kilometer particle detector deployed deep within the South Pole glacier, announced the first detection of an astrophysical flux of high-energy neutrinos in the TeV-PeV range. This breakthrough discovery has prompted a wide-ranging observational effort aimed at identifying the sources of the neutrino flux by combining IceCube measurements with observations spanning the entire electromagnetic spectrum. Gamma rays in particular provide a powerful tool to search for neutrino source counterparts as both particles are produced in high-energy hadronic interactions. The detection and study of neutrino sources would not only signify the start of a new form of astronomy, but could also solve long-standing questions in high-energy astrophysics such as the origin of high-energy cosmic rays. This talk will introduce the IceCube detector, summarize recent results from multi-messenger searches of neutrino sources and present an overview of current and future gamma-ray follow-up observations, especially with the Cherenkov Telescope Array, a ground-based facility for very-high-energy gamma-ray astronomy currently under construction.