Switch to last-active tab in VIM

Put this in your .vimrc:

if !exists('g:lasttab')
  let g:lasttab = 1
endif
nmap <Leader>tl :exe "tabn ".g:lasttab<CR>
au TabLeave * let g:lasttab = tabpagenr()

Then, in normal mode, type \tl to swap to the tab you viewed last.

I use buffers and not tabs, but I am able to switch between the current and latest used buffer using :b#
Basics of using buffers are:

:e filename to open file in new buffer  
:bn to go to next buffer  
:bp to go to previous buffer  
:bd to close current buffer 

Fix the potential issue when a tab is closed:

" Switch to last-active tab
if !exists('g:Lasttab')
    let g:Lasttab = 1
    let g:Lasttab_backup = 1
endif
autocmd! TabLeave * let g:Lasttab_backup = g:Lasttab | let g:Lasttab = tabpagenr()
autocmd! TabClosed * let g:Lasttab = g:Lasttab_backup
nmap <silent> <Leader>` :exe "tabn " . g:Lasttab<cr>