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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.