Modeling and simulation have been extensively used to solve a wide range of problems in structural engineering. However, many simulations require significant computational resources, resulting in exponentially increasing computational time as the spatial and temporal scales of the models increase. This is particularly relevant as the demand for higher fidelity models and simulations increases. Recently, the rapid developments in artificial intelligence technologies, coupled with the wide availability of computational resources and data, have driven the extensive adoption of machine learning techniques to improve the computational accuracy and precision of simulations, which enhances their practicality and potential. In this paper, we present a comprehensive survey of the methodologies and techniques used in this context to solve computationally demanding problems, such as structural system identification, structural design, and prediction applications. Specialized deep neural network algorithms, such as the enhanced probabilistic neural network, have been the subject of numerous articles. However, other machine learning algorithms, including neural dynamic classification and dynamic ensemble learning, have shown significant potential for major advancements in specific applications of structural engineering. Our objective in this paper is to provide a state-of-the-art review of machine learning-based modeling in structural engineering, along with its applications in the following areas: (i) computational mechanics, (ii) structural health monitoring, (iii) structural design and manufacturing, (iv) stress analysis, (v) failure analysis, (vi) material modeling and design, and (vii) optimization problems. We aim to offer a comprehensive overview and provide perspectives on these powerful techniques, which have the potential to become alternatives to conventional modeling methods.