Getting the Covers right with Calilbre

I am new to this forum, to Calibre, and to ebooks in general. I am not new to computers, files, networks, etc.

I have been using Calibre to successfully convert and manage ebooks for both a Kindle and an iPad. (MOBI and Epub)

BUT.......

I don't seem to be able to consistently get the COVERS of the books to display in either format.

I see the covers in Calibre, and can select, change, etc.

SOMETIMES the covers I see in Calibre display in the libraries on the devices.....sometimes they don't.

SOMETIMES the covers are actually IN the books when they are opened but still don't display in the libraries.

I don't seem to be able to find a process path to always have the covers show on the books when they are in the libraries of the devices.

If this subject has been done and done to death, I beg your patience to have someone explain it once more.

Thank you.

jp