  In this article, we review some aspects of gravitational field and cosmology
based on Finsler and Finsler-like generalized metric structures. The
geometrical framework of these spaces allows further investigation of
locally-anisotropic phenomena related to the gravitational field and
cosmological considerations, e.g the extracted geodesics, deflection of light,
Finsler-Einstein gravitational field equations , the Friedmann equations and
the Raychaudhuri equations include extra anisotropic terms that in the
Riemannian framework of General Relativity (GR) are not interpreted. This
approach gives us the opportunity to extend the research with more degrees of
freedom on the tangent bundle of a spacetime manifold. In the above mentioned
generalizations omitting the extra anisotropic terms we recover the framework
of GR. In addition, we study the gravitational Magnus effect in a generalized
metric framework.
  Based on this approach, we describe further properties of Finsler-Randers
(FR) and Schwarzschild Finsler Randers (SFR) cosmological models which are
useful for the description and evolution of the universe.
