  In this paper, we briefly review highlights of nonlocal de Sitter gravity
based on the nonlocal term $ \sqrt{R - 2\Lambda}\ \mathcal{F}(\Box)\ \sqrt{R -
2\Lambda }$ in the Einstein-Hilbert action without matter sector. This nonlocal
de Sitter gravity model has several exact cosmological FLRW solutions and one
of these solutions contains some effects that are usually assigned to dark
matter and dark energy. There are also some other interesting and promising
properties of this kind of gravity nonlocality. We also review some anisotropic
cosmological solutions, and mention the corresponding nonlocal Schwarzschild-de
Sitter metric.
