Currently, the age structure of the world population is changing due to declining birth rates and increasing life expectancy. As a result, physicians worldwide have to treat an increasing number of age-related diseases, of which neurological disorders represent a significant part. In this context, there is an urgent need to discover new therapeutic approaches to counteract the effects of neurodegeneration on human health, and computational science can be of pivotal importance for more effective neurodrug discovery. The knowledge of the molecular structure of the receptors and other biomolecules involved in neurological pathogenesis facilitates the design of new molecules as potential drugs to be used in the fight against diseases of high social relevance such as dementia, Alzheimer’s disease (AD) and Parkinson’s disease (PD), to cite only a few. However, the absence of comprehensive guidelines regarding the strengths and weaknesses of alternative approaches creates a fragmented and disconnected field, resulting in missed opportunities to enhance performance and achieve successful applications. This review aims to summarize some of the most innovative strategies based on computational methods used for neurodrug development. In particular, recent applications and the state-of-the-art of molecular docking and artificial intelligence for ligand- and target-based approaches in novel drug design were reviewed, highlighting the crucial role of in silico methods in the context of neurodrug discovery for neurodegenerative diseases.