  Leading logarithms (LLs) in massless non-renormalizable effective field
theories (EFTs) can be computed with the help of non-linear recurrence
relations. These recurrence relations follow from the fundamental requirements
of unitarity, analyticity and crossing symmetry of scattering amplitudes and
generalize the renormalization group technique for the case of
non-renormalizable EFTs. We review the existing exact solutions of non-linear
recurrence relations relevant for field theoretical applications. We introduce
the new class of quantum field theories (quasi-renormalizable field theories)
in which the resummation of LLs for $2 \to 2$ scattering amplitudes gives rise
to a possibly infinite number of the Landau poles.
