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We review nonsingular static, spherically symmetric solutions of generalrelativity with a minimally coupled scalar field $\phi$ as a source. Consideredare wormholes and regular black holes without a center, including blackuniverses (black holes with an expanding cosmology beyond the horizon). Suchconfigurations require a "ghost" field with negative kinetic energy, but it maybe negative in a restricted (strong-field) region of space and positive outsideit ("trapped ghost") thus explaining why no ghosts are observed under usualconditions. Another possible explanation of the same may be a rapid decay of aghost field at large radii. Before discussing particular examples, some generalresults are presented, such as the necessity of anisotropic matter forobtaining asymptotically flat or anti-de Sitter wormholes, no-hair and globalstructure theorems for black holes with scalar fields. The stability propertiesof scalar wormholes and regular black holes are discussed for perturbationspreserving spherical symmetry. It is stressed that the effective potential$V_{eff}$ for perturbations has universal shapes near generic wormhole throats(a positive pole regularizable by a Darboux transformation) and near transitionsurfaces from canonical to ghost behavior of the scalar field (a negative poleat which the perturbation finiteness requirement plays a stabilizing role). Itis also found that positive poles of $V_{eff}$ emerging at "long throats" (withthe spherical radius $r \approx r_0 + {\rm const} \cdot x^{2n}$, $n > 1$, if$x=0$ is the throat) may be regularized by repeated Darboux transformations forsome values of $n$.

Scalar fields as sources for wormholes and regular black holes