The main pathological symptoms of Alzheimer's disease (AD) are β-amyloid (Aβ) lesions and intracellular neurofibrillary tangles of hyperphosphorylated tau protein. Unfortunately, existing symptomatic therapies targeting Aβ and tau remain ineffective. In addition to these pathogenic factors, oxidative DNA damage is one of the major threats to newborn neurons. It is necessary to consider in detail what causes neurons to be extremely susceptible to oxidative damage, especially in the early stages of development. Accordingly, the regulation of redox status is crucial for the functioning of neural stem cells (NSCs). The redox-dependent balance, of NSC proliferation and differentiation and thus the neurogenesis process, is controlled by a series of signalling pathways. One of the most important signalling pathways activated after oxidative stress is the DNA damage response (DDR). Unfortunately, our understanding of adult neurogenesis in AD is still limited due to the research material used (animal models or post-mortem tissue), providing inconsistent data. Now, thanks to the advances in cellular reprogramming providing patient NSCs, it is possible to fill this gap, which becomes urgent in the light of the potential of their therapeutic use. Therefore, a decent review of redox signalling in NSCs under physiological and pathological conditions is required. At this moment, we attempt to integrate knowledge on the influence of oxidative stress and DDR signalling in NSCs on adult neurogenesis in Alzheimer's disease.