In this review we first present an introduction to He-3 and to the ROTA col
laboration under which most of the knowledge on vortices in superfluid He-3
has been obtained. In the physics part, we start from the exceptional prop
erties of helium at millikelvin temperatures. The dilemma of rotating super
fluids is presented. In He-4 and in He-3-B the problem is solved by nucleat
ing an array of singular vortex lines. Their experimental detection in He-3
by NMR is described next. The vortex cores in He-3-B have two different st
ructures, both of which have spontaneously broken symmetry. A spin-mass vor
tex has been identified as well. This object is characterized by a flow of
spins around the vortex line, in addition to the usual mass current. A grea
t variety of vortices exist in the-A phase of He-3; they are either singula
r or continuous, and their structure can be a line or a sheet or fill the w
hole liquid. Altogether seven different types of vortices have been detecte
d in He-3 by NMR. We also describe briefly other experimental methods that
have been used by ROTA scientists in studying vortices in He-3 and some imp
ortant results thus obtained. Finally, we discuss the possible applications
of experiments and theory of He-3 to particle physics and cosmology. In pa
rticular, we report on experiments where superfluid He-3-B was heated local
ly by absorption of single neutrons. The resulting events can be used to te
st theoretical models of the Big Bang at the beginning of our universe.