Disclaimer: All methods commonly used by agile teams have their specific advantages and disadvantages. Ideally, an agile team is empowered and self-organized and can choose the methods and frameworks that are the best fit for their work.
Depending on different industries (manufacturing, software development, document development, etc.), other methods are applied and sometimes combined with the below-mentioned methods.
Scrum
Agile framework providing some structure for teams to efficiently collaborate. It helps “people, teams and organizations generate value through adaptive solutions for complex problems” (source: https://scrum.org). It consists of a set of specific functional roles which act together according to defined rules. See https://scrumguides.org/scrum-guide.html for further details and more background information.
Kanban (Japanese: meaning signboard, or billboard)
A lean method/strategy to manage and improve working in teams, which originates in lean manufacturing. “This approach aims to manage work by balancing demands with available capacity, and by improving the handling of system-level bottlenecks” (source: https://en.wikipedia.org/wiki/Kanban_(development)) and focuses on optimizing the flow of value. It uses a visual, pull-based system, including the visualization of a workflow, the (pro-)active management of the items in a workflow, and on improving the workflow. See https://kanbanguides.org/english/ for further details and more background information.
Lean development / lean writing
The lean concept is used to focus deliverables (e.g. documents) on the key content only and to remove all superfluous, non-value-adding information. Originally invented as lean manufacturing by Toyota, the concept has spread widely across industries. Applying lean writing practices, results in deliverables maximally tailored to the primary audience and the primary aims of the deliverable. It can be easily combined with agile methods. Also see the Regulatory Matters section of the EMWA Journal on Social media (https://journal.emwa.org/social-media/regulatory-matters/). See https://www.theleansixsigmacompany.co.uk/what-is-lean/ for further details and more background information on the entire concept.