There are two current choices:
1 - Use "Options -> Export to File". This will export the entire
history, which can then be loaded into your own local copy of Galaxy
any other Galaxy instance that you have access to) for review. If you
only want portions of a particular history, first copy those items
a new history ("Options -> Copy Datasets"), then export the history
that limited set.
2 - Click on the disc icon for each dataset that you want to download
and save. You should be able to queue up a few overlapping download
processes at the same time. When overlapping, this will slow them
but you won't need to wait for one to finish, then start the next, and
If you find that the downloads are failing due to large data size(s),
you can try unix tools such as wget or curl. This will work for both
exported histories and individual datasets. For histories, the link is
provided, so that can be directly copied. For datasets, right click on
the disc icon and use "Copy Link Address.". Then use this syntax:
% wget '<link>'
% curl -O '<link>'
Hopefully one of these options will work out for you,