Every research you start lives in All Research. From the list you can find a research, move research between projects and delete what you are done with. Refreshing happens on the research itself.
Find a research
Each row shows the keyword, how many pieces of content were created from it, its search intent and format, its project and when it was last updated. The top of the list shows how many research credits you have left.
Once you have four research runs or more, a filter strip appears:
Search keywords narrows the list as you type.
Status pills filter by where each research stands: Running, Needs input, Complete, Failed or Not run. A pill only shows up when some research has that status.
All intents, All formats and All projects filter by search intent, format and project. Each one only appears when your research has more than one value for it.
A research that needs input is waiting for you to pick its intent and format. See choosing a search intent and format.

Move research to another project
Each row's icon doubles as a checkbox. Tick the research you want, or use Select all to take everything in the filtered list. A bar appears with the number selected.
Click Move and pick a project. In a project's own research list, that project is ticked and cannot be picked, and Unfiled (remove from project) takes them out of it.
Delete research
Select the research and click Delete, or open one and delete it from there. Once you confirm, its SERP data, outline and findings are removed.
Content you created from a deleted research is not deleted. It keeps living, and the research is simply no longer attached to it.
Deleting research cannot be undone, and it does not return the research credit it spent.
A research that is still running cannot be deleted. Open it and click Cancel run first.
Refresh a finished research
Search results change. To bring a research up to date, open it and click the refresh icon at the top right (its tooltip starts "Refresh this research"), then confirm with Refresh research.
A refresh replaces the SERP data and regenerates the recommended outline. It reuses the intent and format you picked, so it does not stop to ask again. Your edited outline is kept, and content created from the research keeps it attached.
A refresh uses one research credit, charged when it succeeds. With no credits left, Refresh research in the confirmation stays disabled.