The goal is to bring together an in-depth analysis of physics-based deep learning approaches in transportation domains and classify them according to their applicability. To carry out the systematic literature search, a Preferred Reporting Items for Systematic Reviews and Meta-Analysis flowchart is used with certain inclusion and exclusion criteria. Different keyword searches are carried out in the Scopus and Web of Science databases, followed by relevant references and citation analyses to find eligible papers subject to a full-text peer review. Finally, the classification and analysis of these papers take place based on their applicability. 141 and 39 records were found by the initial database search and referencing and citation analysis respectively. A total of 65 documents were selected to carry out full-text reviews, and finally, 35 documents were included in the study. Based on the applications of physics-informed deep learning in transportation engineering, the authors classified the literature into three major categories: 1) safety assessment and safety analysis, 2) model preparation, and 3) prediction and estimation. Finally, this research also provides the challenges and future directions in this emerging field.