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The covariant density functional theory (CDFT) is mature microscopic
theory for studies in low-energy nuclear physics. In its framework
the nucleus is described as a system of nucleons which interact
via the exchange of different mesons. In my presentation, I will
focus on recent studies of different nuclear phenomena across the
nuclear chart and its extremes within the CDFT framework. I will
start with the discussion of basic principles of this theory. Then
I will focus on the clusterization in light nuclei at zero and high
spins and on microscopic origin of this phenomenon. This will be
followed by the discussion of neutron-rich nuclei, theoretical
uncertainties in their description and their role in the crust
of neutron stars. The variation of the composition of the crust
of neutron stars with depth will be discussed. Finally, the physics
of hyperheavy (Z>126) nuclei and the structure of nuclear landscape
at this extreme will be discussed.
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