Here are some apps and tricks that may be useful for researchers. (Please do comment or add so we can share how to make the iPad work well for research. Another blog focuses on iPadPro for handwriting.)
Sync & store local files on iPad and directory structure
It may be old-fashioned, but I do like off-line access to my files. There must be some iOS restriction so that cloud storage providers (e.g, Dropbox and OneDrive) cannot just make local copies of entire directories onto the iPad. Using Dropbox and OneDrive you are restricted to selecting individual files (one-by-one) and clicking “Make Available Offline.” (It would be AWESOME if Dropbox and OneDrive would simply, by default as they do on Mac and PC, make local copies of entire folders and sync whenever connected to the Internet, but alas…).
The free app Document (by Readdle) provides a solution: it connects to your cloud storage apps and you can click entire folders and click “Sync” in upper right “to enable two-way synchronization.” It will automatically include subfolders in the sync. GREAT. The app also views many file types, including media files.
There are many PDF apps that may work well for you. After I found Documents, I got hooked on PDF Expert. This $9.99 app is also made by Readdle and integrates flawlessly and uses the same file structure (including directory synching). In addition to usual text markup (in all ways you can imagine), it also works perfectly with Apple Pencil for beautiful pen markup. So it meets my two objectives: easy file management and handwriting.
Organizing research ideas and projects
If visual file structure appeals to you, consider Microsoft OneNote. I love the 3-tier hierarchical structure: I have a Notebook for Research, Teaching, Seminars and Service. Within each notebook, you have various folders (say one per course that you teach). And within each folder, various pages (say one per class of your course). It synchs automatically over the cloud with your iPhone and Mac, and with PC. And handwriting works fairly well.
Writing research articles in Latex
Cloud and web-based Latex tools like ShareLatex work well on the iPad. If you also want off-line access and compilation, consider the $15 Texpad. A nice feature is that it connects and synchs to one specific Dropbox folder. In Texpad, I clicked “dropbox” on left side, and clicked “+” to write a new simple test *.tex on iPad. This directly created the folder \Apps\Texpad on Dropbox and everything syncs automatically. Thus, just move your active *.tex files to the root directory Apps\Texpad in your Dropbox folder. Colleagues told me that the Mac version of texpad is also excellent.