Despite several successful applications, structural health monitoring (SHM) of bridges is still in its exploratory phase and, despite the increase in research, many challenges remain in order for it to become a commonplace practice in civil engineering. New SHM approaches have emerged sparked by the massive amount of acquired experimental monitoring data and breakthroughs in technology, computing capability and data storage solutions. To this end, the data-based approaches, mostly by resorting to machine learning techniques, have shown to be promising. This work proposes an unsupervised learning approach based on feedforward artificial neural networks for damage identification and condition monitoring of railway bridges. The inputs and output of the algorithm typically consist of measured accelerations in the bridge deck due to train passages, measurements which can be acquired easily with few installed sensors. Based only on data and statistical analysis, alarms with reference to early damage in the bridge can be triggered by the deployed SHM system. The implementation of the proposed approach is demonstrated and validated with both numerical and experimental case studies, where different aspects with relevance to SHM are as explored.