This paper presents a comprehensive overview of modelling, simulation and implementation of neural networks, taking into account that two aims have emerged in this area: the improvement of our understanding of the behaviour of the nervous system and the need to find inspiration from it to build systems with the advantages provided by nature to perform certain relevant tasks. The development and evolution of different topics related to neural networks is described (simulators, implementations, and real-world applications) showing that the field has acquired maturity and consolidation, proven by its competitiveness in solving real-world problems. The paper also shows how, over time, artificial neural networks have contributed to fundamental concepts at the birth and development of other disciplines such as Computational Neuroscience, Neuro-engineering, Computational Intelligence and Machine Learning. A better understanding of the human brain is considered one of the challenges of this century, and to achieve it, as this paper goes on to describe, several important national and multinational projects and initiatives are marking the way to follow in neural-network research.