Brain damage can be induced by oxygen deprivation. It is known that hypoxic or anoxic conditions can lead to changes in the expression levels of non-coding RNAs (ncRNAs), which, in turn, can be related to Central Nervous System (CNS) injuries. Therefore, it could be useful to investigate the involvement of non-coding RNAs (ncRNAs), as well as the underlying mechanisms which are able to modulate them in brain damage induced by hypoxic or anoxic conditions. In this review, we focused on recent research that associates these conditions with long non-coding RNAs (lncRNAs) and circular RNAs (circRNAs). The results of this review demonstrate that the expression of both lncRNAs and circRNAs can be influenced by oxygen deprivation conditions and so they can contribute to inducing damage or providing neuroprotection by affecting specific molecular pathways. Furthermore, several experimental studies have shown that ncRNA activity can be regulated by compounds, thus also modifying their transcriptomic profile and their effects on CNS damages induced by hypoxic/anoxic events.