A fellow is a member of a group of people who work together in a fellowship pursuing mutual knowledge or practice. There are many different kinds of fellowships which are awarded for different reasons in academia and industry, often indicating an advanced level of scholarship.
The title of research fellow is used to denote an academic research position at a university or a similar institution and is roughly equivalent to the title of lecturer in the teaching career pathway. Research fellow is also used to refer to the holder of a research fellowship. These are often shortened to the name of the programme or organisation, e.g. Dorothy Hodgkin Fellow rather than Dorothy Hodgkin Research Fellow, except where this might cause confusion with another fellowship, e.g. Royal Society University Research Fellowship).
In the context of graduate school in the United States and Canada, a fellow is a recipient of a postgraduate fellowship. Examples include the NSF Graduate Research Fellowship, the National Defense Science and Engineering Graduate Fellowship, the Guggenheim Fellowship, the Rosenthal Fellowship, Woodrow Wilson Teaching Fellowship and the Presidential Management Fellowship. It is granted to prospective or current students, on the basis of their academic or research achievements.
In the UK, research fellowships are awarded to support postdoctoral researchers such as those funded by the Wellcome Trust and the Biotechnology and Biological Sciences Research Council (BBSRC). At ETH Zurich, postdoctoral fellowships support incoming researchers. The MacArthur Fellows Program (aka "genius grant") as prestigious research fellowship awarded in the United States.