The minimal non-decreasing function f : N → N such that every word w vanishing in a group G = hA | Ri and having length ||w|| ≤ n is freely equal to a product of at most f(n) conjugates of relators from R, is called the isoperimetric or Dehn function of the presentation G = hA | Ri. By van Kampen Lemma, f(n) is equal to the maximal area of minimal diagrams _ with ||@_|| ≤ n. For finitely presented groups (i.e., both sets A and R are finite) isoperimetric functions are usually taken up to equivalence to get rid of the dependence on a finite presentation for G. To introduce this equivalence ∼, we write f _ g if there is a positive integer c such that f(n) ≤ cg(cn) cn for any n ∈ N. Two non-decreasing functions f and g on N are called equivalent if f _ g and g _ f. Almost complete description of rapidly increasing isoperimetric functions (at least biquadratic) and the connection to the computation complexity of the word problem in groups can be found in [9], [1] and [7]. In fact, a subquadratic isoperimetric functions of finitely presented group G is linear up to equivalence, and the isoperimetric function of G is equaivalent to linear function if and only if the group G is hyperbolic (see [3, 6.8.M], [5], [2]). The speaker will discuss the asymptotic behavior of isoperimetric functions close to quadratic ones. In particular, he will pay attention to his recent results.