  Diophantine exponents are ones of the simplest quantitative characteristics
responsible for the approximation properties of linear subspaces of a Euclidean
space. This survey is aimed at describing the current state of the area of
Diophantine approximation which studies Diophantine exponents and relations
they satisfy. We discuss classical Diophantine exponents arising in the problem
of approximating zero with the set of the values of several linear forms at
integer points, their analogues in Diophantine approximation with weights,
multiplicative Diophantine exponents, and Diophantine exponents of lattices. We
pay special attention to the transference principle.
