Hitchhiker's guide to fellowships in academia
This post is not meant to give a super detailed vision of the possibilities of the so called "middleman" of academia.
However, it tries to give you some names you can write down in your list or that you can google to get a better idea on what you can find around the world (I would bet this list is not nearly close to 30% of the whole).
The list is a reflection on my own knowledge (I am a postdoc in astrophysics) and the connections I have made during my time as PhD student and postdoc. You should see the list below as the first points you can discovered in a "treasure map" hoping it will help you in your hunt and encourage you to find new pieces and new possibilities.
List of General Fellowships for Physics and Maths PDRA/PhD
Royal Commission for the Exhibition of 1851 Research Fellowships (Feb.) - No more than 3 years postdoctoral experience - 3 years duration
Leverhulme Trust Early-Career Research Fellowships (Mar.) - max 5 yrs since PhD - 3 yrs fellowship
EPSRC Fellowships (Postdoctoral and Early Career) - Rolling 3 years (PD) or 5 years (EC) duration
Royal Society Dorothy Hodgkin Fellowship (Jan.) - flexible working pattern - Female candidates are particularly invited to apply - 5 years duration
RSE / Scottish Govt Personal Fellowships (Mar.) - 2 to 6 years postdoctoral experience - Must be able to spend up to one year outside of the UK - 5 years duration
STFC Ernest Rutherford Fellowships (Sep.) - Minimum 2 years postdoctoral experience - 5 yrs duration
Royal Society University Research Fellowship (Sep.) -Must have 3-8 years postdoctoral experience - 5 years duration with possibility of extending a further 3 years - 12% success rate
NERC Independent Research Fellowships (Oct.) - Max of 8 years from the PhD - 5 years duration
Daphne Jackson Fellowships - Rolling - A career break of at least two years’ duration taken for family, caring or health reasons - Carried out over 2 years flexibly
Royal Commission for the Exhibition of 1851 Industrial Fellowships (Jan.) - nominated by a sponsoring company - up to 3 yrs
Royal Society Newton International Fellowship (Mar.) - no more than 7 years of postdoc - Must be working outside the UK and not hold UK citizenship - 2 years
Marie Skłodowska -Curie Individual Fellowships (Sep.) - Cannot have worked in country of the host institution for more than 12 months of previous 3 years - 2 year duration
Marie Skłodowska -Curie Action Fellowships (COFUND type) -Cannot have worked in country of the host institution for more than 12 months of previous 3 years - 3 year duration
50th Bath Prize Fellowship - 5 years - most likely only one appearance but ther ewill be other similar in the world, so watch this kind of fellowships
List of Fellowships in European countries
Swiss:
Branco-Weiss-Fellowship - 5 years, host institution needs to be in Switzerland, PhD less than 5 years before, younger than 35.
Germany:
Max Planck Research Groups - 5 years
Emmy Noether program - 5 years
Freigeist-Fellowships - 5 years duration and no more than 5 years from PhD
Netherlands:
Veni-Vidi-Vici - Veni for 0-3 years after PhD, Vidi for 4-8 years after PhD, Vici for 9-15 years after PhD.
France:
L'Oreal
AXA
Sweden:
Vetenskapsrådet - 4 years funding, two calls per year
Finnish:
Academy of Finland - 5 years, 3 years from PhD
Canada:
Banting - 2 years
List of Astronomy Fellowships
ESO Fellowship - 3 years (Oct.) - Garching (Germany) or Santiago (Chile) where you will have an extra 4th year to spend whenever you want in Eutrope - no restrictions but they tend to hire PDRA within 3-4 years since PhD
ESA Fellowship - 3 years (Netherlands)
Royal Astronomical Society Fellowship - 3 years (Oct in UK), no more than 5 years since PhD
Dennis Sciama Fellowship - 3 years (Oct.), cosmology related at the ICG of Portsmouth
Rymdstyrelsen Fellowship - Sweden - mainly related to detectors and observational astronomy
Newton Fellowship 3 years - max 3 years since PhD
Sagan Fellowship 3 years - max 3 years since PhD
Einstein Fellowship 3 years - max 3 years since PhD
Chandra Fellowship 3 years - max 3 years since PhD
Hubble Fellowship 3 years - max 3 years since PhD
Cassini Fellowship 3 years - max 3 years since PhD
Jansky Fellowship 3 years - max 3 years since PhD
Dunlap Fellowship - Toronto - 3 years
CITA - 2 per years, one inToronto, the other everywhere in Canada - 3 years
Carnagie Fellowship USA (Nov.) - 3 years - not every year
Carnagie-Princeton Fellowship USA (Nov.) - 4 years (?) - not every year
Carnegie Mellon University - McWilliams Fellowship not every year
Dark Cosmology Center DARK Fellowships not every year
ETH Zurich Zwicky prize fellowship 3 years (?) (Jan.)
+ several others to add