  The aim of this review is to discuss the ways to obtain results based on
gravity with higher derivatives in D-dimensional world. We considered the
following ways: (1) reduction to scalar tensor gravity, (2) direct solution of
the equations of motion, (3) derivation of approximate equations in the
presence of a small parameter in the system, and (4) the method of test
functions. Some applications are presented to illustrate each method. The
unification of two necessary elements of a future theory is also kept in mind -
the extra dimensions and the extended form of the gravity.
