Who can apply for research grants in Europe? Are there some degree requirements? Can students (undergraduate/graduate) apply for research grants? I know that the answer surely depends on the institution giving the grant, but I assume there are some general requirements, formal or informal. If you know (or even better, are) a student who has received a research grant, please tell how difficult it was. To clarify, I'm not asking about funding to do some degree, but funding to establish new research projects.
Rules will very strongly depend on the funding institution you're applying to, and even on the details of the grant program. Eligibility criteria are listed in each funding program, so go check up those programs that are of interest to you. Even restricting to “in Europe” doesn't help much, because Europe is a large continent with very heterogeneous research (and funding) institutions.
Regarding students (undergraduate or graduate), the only types of grants I can think of are:
- grants to fund your degree; for example, getting a fellowship that would fund you during your PhD
- grants that encourage international collaboration and exchange; e.g., the Chateaubriand fellowship to spend some months in a French lab, or JSPS fellowship for short stays in Japan.
A student is expected to devote his efforts to the project for which he is employed, not to bid for new research projects on their own. Thus, I don't think you can get funding for a new research project of your own, until you are an independent researcher.
Most grant programs target institutions - while a grant proposal will generally be prepared by a particular principal investigator (and possibly their team) according to their individual research experience and research goals, and the grant evaluation might place a large importance on their CV and individual publication history, in these programs the grant application has to be submitted by a qualified institution, and the grant will be awarded to that institution, not to an individual.
Furthermore, many grant programs require multiple institutions to apply - e.g. Horizon 2020 calls tend to require consortiums representing multiple EU countries; various grants for applied research require a participation of both a research institution and an industry partner, etc.
There are some types of grants that are targeted at individual researchers, e.g. European Research Council or some post-doc programs. However, the general assumption is that the doctor's degree is the basic qualification showing that someone is qualified to do independent unsupervised research. The grants tend to be quite competitive, so a PhD degree by itself is nowhere near sufficient, but it's a basic 'table stakes' requirement that's mandatory in almost all (or all?) research grant programs.