  This paper gives an overview of the properties of all possible equilibrium
sequences of compact strange-matter stars with nuclear crusts, which range from
strange stars to strange dwarfs. In contrast to their non-strange counterparts,
--neutron stars and white dwarfs--, their properties are determined by two
(rather than one) parameters, the central star density and the density at the
base of the nuclear crust. This leads to stellar strange-matter configurations
whose properties are much more complex than those of the conventional sequence.
As an example, two generically different categories of stable strange dwarfs
are found, which could be the observed white dwarfs. Furthermore we find very
low-mass strange stellar objects, with masses as small as those of Jupiter or
even lighter planets. Such objects, if abundant enough in our Galaxy, should be
seen by the presently performed gravitational microlensing searches. Further
aspects studied in this paper concern the limiting rotational periods and the
cooling behavior of neutron stars and their strange counterparts.
