This review presents the analysis and systematization of modern data on the molecular mechanisms of autism spectrum disorders (ASD) development. Polyetiology and the multifactorial nature of ASD have been proved. The attempt has been made to jointly review and systematize current hypotheses of ASD pathogenesis at the molecular level from the standpoint of aberrant brain plasticity. The mechanism of glutamate excitotoxicity formation, the effect of imbalance of neuroactive amino acids and their derivatives, neurotransmitters, and hormones on the ASD formation have been considered in detail. The strengths and weaknesses of the proposed hypotheses have been analyzed from the standpoint of evidence-based medicine. The conclusion has been drawn on the leading role of glutamate excitotoxicity as a biochemical mechanism of aberrant neuroplasticity accompanied by oxidative stress and mitochondrial dysfunction. The mechanism of aberrant neuroplasticity has also been traced at the critical moments of the nervous system development taking into account the influence of various factors of the internal and external environment. New approaches to searching for ASD molecular markers have been considered.