The food supply chain (FSC) is made up of producers, traders and processors who bring the product from supply to demand through logistical processes. Food supply chains require specific methodologies for their current diagnosis, evaluation and improvement. Logistics in food supply chain requires to be managed according to its nature. This article identifies the different methodologies through a systematic literature review of publications from 2005 to 2022, using Web of Science, Scopus and Google Scholar search engines, in order to establish the state of the art. As a result of this review, a new taxonomy is proposed and includes the following methodological groups: management, qualitative, quantitative, multi-criteria decision-making (MCDM), statistics, machine learning, mathematical modelling, discrete simulation, system dynamics and others. The methodologies of characterization, evaluation and improvement are classified into two main groups of logistical means and modes. The performance measures most commonly used in the methodologies by the researchers were also identified. From the article, discussions, challenges and trends are generated to identify possible future research and different gaps.