  The present article proposes a review of the most recent results obtained in
the study of Novikov's problem on the description of the geometry of the level
lines of quasi-periodic functions in the plane. Most of the paper is devoted to
the results obtained for functions with three quasi-periods, which play a very
important role in the theory of transport phenomena in metals. In this part,
along with previously known results, a number of new results are presented that
significantly refine the general description of the picture that arises in this
case. New statements are also presented for the case of functions with more
than three quasi-periods, which open up approaches to the further study of
Novikov's problem in the most general formulation. The role of Novikov's
problem in various fields of mathematical and theoretical physics is also
discussed.
