  There is accumulating evidence that (fundamental) scalar fields may exist in
Nature. The gravitational collapse of such a boson cloud would lead to a boson
star (BS) as a new type of a compact object. Similarly as for white dwarfs and
neutron stars, there exists a limiting mass, below which a BS is stable against
complete gravitational collapse to a black hole. According to the form of the
self-interaction of the basic constituents and the spacetime symmetry, we can
distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs.
Their compactness prevents a Newtonian approximation, however, modifications of
general relativity, as in the case of Jordan-Brans-Dicke theory as a low energy
limit of strings, would provide them with gravitational memory. In general, a
BS is a compact, completely regular configuration with structured layers due to
the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical
mass inversely proportional to constituent mass, an effective radius, and a
large particle number. Due to the Heisenberg principle, there exists a
completely stable branch, and as a coherent state, it allows for rotating
solutions with quantised angular momentum. In this review, we concentrate on
the fascinating possibilities of detecting the various subtypes of (excited)
BSs: Possible signals include gravitational redshift and (micro-)lensing,
emission of gravitational waves, or, in the case of a giant BS, its dark matter
contribution to the rotation curves of galactic halos.
