I track my supplier's forms in an Excel spreadsheet. I have a column for each form, and fill the cells with the date on the form. I have conditional formatting setup to highlight the cells yellow when the date in that cell is 6 months away from three years old, and then dark orange when it is past three years (we have a triennial requirement to resubmit all our vendor forms for updates). Items like the COI or GFSI cert that expires each year gets a different conditional format to use.
I'm sure there are better ways, but at least I can review my many suppliers at a glance and then go digging into the folders if I need something. Also helps to prove to an auditor that I've reviewed the files, as I have to open them to get the printed/written date to place on my spreadsheet.