The entire review intends to give a general introduction to deep learning approaches for Structural Health Monitoring (SHM) and damage detection in civil infrastructure. Damage detection has to be done accurately and timely to take safety, reliability, and long service out of account into considerations of infrastructural systems. In contrast to conventional SHM methods, this technique is much better, especially when dealing with large-scale data and automatic feature extraction from complex data. Also discussed are some limitations of deep learning methods that make them less feasible for some applications—a need for large quantities of labelled data, huge computational costs, and generalization problems. Lastly, the review discusses future directions on the given topic and proposes potential mechanisms to counter such limitations to bolster the scope and performance of SHM systems based on deep learning.