  The existence of localized, approximately stationary, lumps of the classical
gravitational and electromagnetic field -- $geons$ -- was conjectured more than
half a century ago. If one insists on exact stationarity, topologically trivial
configurations in electro-vacuum are ruled out by no-go theorems for solitons.
But stationary, asymptotically flat geons found a realization in scalar-vacuum,
where everywhere non-singular, localized field lumps exist, known as (scalar)
boson stars. Similar geons have subsequently been found in Einstein-Dirac
theory and, more recently, in Einstein-Proca theory. We identify the common
conditions that allow these solutions, which may also exist for other spin
fields. Moreover, we present a comparison of spherically symmetric geons for
the spin $0,1/2$ and $1$, emphasising the mathematical similarities and
clarifying the physical differences, particularly between the bosonic and
fermonic cases. We clarify that for the fermionic case, Pauli's exclusion
principle prevents a continuous family of solutions for a fixed field mass;
rather only a discrete set exists, in contrast with the bosonic case.
