  Possible models of modified gravity are being extensively studied now, with
most phenomenological motivations coming from puzzles and tensions in cosmology
due to a natural desire to better fit the known and newly coming data. At the
same time, available experimental evidence is limited for testing gravity as a
force beyond the regimes in which the theory of general relativity has proven
to be successful. This situation leads researchers to look for ``the simplest
modification'' to general relativity in a certain class of models, which is
enough to solve one or more problems. As a result, we are lost amid a variety
of theories with no deeper guiding principle. We give a general review of
existing approaches and discuss the current state of the art.
