As a process that identifies geologic structures of interest such as faults, salt domes, or elements of petroleum systems in general, seismic structural interpretation depends heavily on the domain knowledge and experience of interpreters as well as visual cues of geologic structures, such as texture and geometry. With the dramatic increase in size of seismic data acquired for hydrocarbon exploration, structural interpretation has become more time consuming and labor intensive. By treating seismic data as images rather than signal traces, researchers have been able to utilize advanced image-processing and machine-learning techniques to assist interpretation directly. In this paper, we mainly focus on the interpretation of two important geologic structures, faults and salt domes, and summarize interpretation workflows based on typical or advanced image-processing and machine-learning algorithms. In recent years, increasing computational power and the massive amount of available data have led to the rise of deep learning. Deep-learning models that simulate the human brain's biological neural networks can achieve state-of-the-art accuracy and even exceed human-level performance on numerous applications. The convolutional neural network — a form of deep-learning model that is effective in analyzing visual imagery — has been applied in fault and salt dome interpretation. At the end of this review, we provide insight and discussion on the future of structural interpretation.