Transport and logistics systems include a range of activities that deal with all sorts of decisions and operations from material handling to vehicle routing. One of the main challenges for transport and logistics processes is to deal with large-scale and complex problems. However, with increasingly diverse sets of operational real-world data becoming available, data-driven heuristic approaches are promising to pave the path for solving the problems in the field of transport and logistics. Thus, a comprehensive review is needed to observe the reflections of this path in literature. To bridge this gap, a total of 40 papers on the topic of "data-driven heuristic approaches to logistics and transportation problems" are determined. Before the categorization and content analysis; descriptive, bibliometric and social network analysis are carried out to identify the current state of the literature. All the papers are systemically reviewed based on different perspectives, namely data-driven methodology, heuristics, sub-problems and etc. Based on the review, suggestions for future research are likewise provided. Subsequently, machine learning and deep learning methods are considered to be among the most promising data-driven methodologies. The review may be useful for academicians, researchers, and practitioners for a better understanding of data-driven heuristic approaches to transportation and logistics problems.