  Along with the construction of non-Lorentz-invariant effective field
theories, recent studies which are based on geometric models of Finsler
space-time become more and more popular. In this respect, the Finslerian
approach to the problem of Lorentz symmetry violation is characterized by the
fact that the violation of Lorentz symmetry is not accompanied by a violation
of relativistic symmetry. That means, in particular, that preservation of
relativistic symmetry can be considered as a rigorous criterion of the
viability for any non-Lorentz-invariant effective field theory. Although this
paper has a review character, it contains (with few exceptions) only those
results on Finsler extensions of relativity theory, that were obtained by the
authors.
