Weather routing has been extensively used as a decision support system in merchant ship operations and traffic management. A critical component of such a system is the optimisation method. Over recent years, substantial research efforts have been devoted to developing voyage optimisation algorithms, either to support decisionmaking of weather routing in merchant shipping or to assist autonomous ships in academic research. The requirements for optimisation methods for merchant shipping differ significantly from those in academic autonomous ship applications. However, many optimisation-related terminologies and algorithms are often used arbitrarily across these two fields, easily leading to confusion. In addition, the emergence of machine learning after 2020 has shown a significant impact on the development of those optimisation algorithms. Still, we see a lack of a systematic review and in-depth summary of recent developments in the optimisation methods focused on weather routing. This paper presents an overview of recent scientific publications to show state-of-the-art research and development status and trends. Focusing on the optimisation methods used in weather routing, we clarify optimisation terminologies. In addition, we propose a general framework to develop voyage optimisation methods to summarise and categorise various developed algorithms. Then, we review scientific papers published in recent years for weather routing developments and applications. Finally, future research and outlooks are discussed for further development of weather routing algorithms.