Export controls apply if the topic of the research appears on either the U.S. Munitions List (ITAR) or the Commerce Control List (EAR). There are exclusions and exceptions to the application of the regulations.
Furthermore, it depends on both the technologies (i.e., the work scope) and the countries (either foreign destinations or foreign personnel) involved. ITAR applies if the subject of the research appears on the ITAR munitions list. Under ITAR, the country of destination is irrelevant; export of a controlled item to any foreign country or any foreign national would be in violation of the law.
The application of EAR is more complicated. It depends on both the technology involved and the country of destination. For example, you might have a technology that can be exported to Canada but not to Venezuela. In most cases, technologies are very precisely defined, and the definitions affect the applicability of the law. For example, telecommunications equipment involving lasers that transmit at wavelengths above 1750 nm may be controlled, while similar equipment using a smaller wavelength is not controlled.
For more information, please use Stanford's Export Control Decision Tree.
More information about what is affected by Export Control