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In the field of quantum chaos, the study of energy levels plays an importantrole. The aim of this review paper is to critically discuss some of the maincontributions regarding the connection between classical dynamics,semi-classical quantization and spectral statistics of energy levels. Inparticular, we analyze in detail degeneracies and quasi-crossings in theeigenvalues of quantum Hamiltonians which are classically non-integrable.Summary: 1. Introduction; 2. Quasi-Crossing and Chaos; 3. MolecularSpectroscopy; 4. Nuclear Models; 4.1 Zirnbauer-Verbaashot-Weidenmuller Model;4.2 Lipkin-Meshow-Glick Model; 5. Particle Physics and Field Theory; 6.Conclusions.Comment: 26 pages, Latex, 9 figures, to be published in International Journal  of Modern Physics

ENERGY LEVEL QUASI-CROSSINGS: ACCIDENTAL DEGENERACIES OR SIGNATURE OF QUANTUM CHAOS?