Maritime transport is the backbone of international trade and globalization. Maritime transport research can be roughly divided into two categories, namely the shipping side and the port side. Most of the classic approaches adopted to address practical problems in these research topics are based on long-term observations and expert knowledge, while few of them are based on historical data accumulated from practice. In recent years, emerging approaches, which we refer to as machine learning and deep learning techniques in this essay, have been receiving a wider attention to solve practical problems. As a relatively conservative industry, there are some initial trials of applying the emerging approaches to solve practical problems in the maritime sector. The objective of this essay is to review the application of emerging approaches to maritime transport research. The main research topics in maritime transport and classic methods developed to solve them are first presented. The introduction of emerging approaches and their suitability to be applied in maritime transport research is then discussed. Related existing studies are then reviewed according to problem settings, main data sources, and emerging approaches adopted. Challenges and solutions in the process are also discussed from the perspectives of data, model, users, and targets. Finally, promising future research directions are identified. This essay is the first to give a comprehensive review of existing studies on developing machine learning and deep learning models together with popular data sources used to address practical problems in maritime transport.