Concrete is one of the most widely used materials in various civil engineering applications. Its global production rate is increasing to meet demand. Mechanical properties of concrete are among important parameters in designing and evaluating its performance. Over the past few decades, machine learning has been used to model real-world problems. Machine learning, as a branch of artificial intelligence, is gaining popularity in many scientific fields such as robotics, statistics, bioinformatics, computer science, and construction materials. Machine learning has many advantages over statistical and experimental models, such as optimal accuracy, high-performance speed, responsiveness in complex environments, and economic cost-effectiveness. Recently, more researchers are looking into deep learning, which is a group of machine learning algorithms, as a powerful method in matters of diagnosis and classification. Hence, this paper provides a review of successful ML and DL model applications to predict concrete mechanical properties. Several modeling algorithms were reviewed highlighting their applications, performance, current knowledge gaps, and suggestions for future research. This paper will assist construction material engineers and researchers in selecting suitable and accurate techniques that fit their applications.