  The Jeffreys model (also associated with the names of Lethersich and Oldroyd)
is one of the crucial conceptions in the theory of viscoelastic fluids. The
models of Jeffreys type describe behaviour of bitumens, blood, polymers and
their solutions, dough, the earth's crust, concrete, lubricants etc. Study of
BVPs corresponding to their statics and dynamics meets a lot of mathematical
difficulties, which turn out to be much harder than the ones that are related
to the celebrated Navier-Stokes system. In this work, we make an attempt to
review the recent results and main unsolved problems for equations of motion
for the mediums of Jeffreys' type.
