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A wide range of cosmological tests indicates that various properties of the Universe can be well explained by the presence of a uniformly dispersed dominant part of the current energetic content, i.e. so-called dark energy. Its basic feature is expressed by cosmic repulsion, causing an accelerated expansion of space, whereas the density of dark energy remains unchanged; in Einstein field equations, dark energy is well described by the cosmological constant (Lambda). Clearly Lambda must be defined not only in Universe evolution, but also in astrophysical processes. Here we introduce some of the astrophysical phenomena of Lambda studied by the relativistic group in Opava, e.g. its influence on the motion of stars in the gravitational field of supermassive black holes, on the motion of dwarf galaxies at the peripheries of giant galaxies, on the form and properties of toroidal configurations of fluid circling around supermassive black holes, or on polytrophic configurations modelling dark matter halos.