The Strategic Research Agenda (SRA; https://www.ejp-eurad.eu/publications/eurad-sra) of the European Joint Programme on Radioactive Waste Management (EURAD; https://www.ejp-eurad.eu/) describes the scientific and technical domains and sub-domains and knowledge management needs of common interest between EURAD participant organizations. Theme number 7 is entitled “Performance assessment, safety case development and safety analyses.” A list of research and development priorities and activities of common interest to be addressed within EURAD for theme 7 have been established. Amongst others, the Understanding and modelling of multi-physical Thermo-Hydro-Mechanical-Chemical coupled processes (THMC) occurring in radioactive waste disposal is a major and permanent issue to support optimization of design and safety case abstraction. To tackle this challenge a research work package entitled “DONUT: Development and improvement of numerical methods and tools for modelling coupled processes” has been conducted within the EURAD join programming initiative. The purpose of this work package is to improve/develop methods or numerical tools in order to go a step further in development of (i) relevant, performant and cutting-edge numerical methods that can easily be implemented in existing or new tools, in order to carry out high-performance computing to facilitate the study of highly coupled processes in large systems, (ii) numerical scale transition schemes for coupled processes, (iii) innovative numerical methods to carry out uncertainty and sensitivity analyses. In this paper the work carried out within the DONUT work package is put in perspective regarding the existing concept and literature on the field. It does not pretend to be exhaustive but rather to put emphasis on particular issues tackled during the project.