InfoPath Dev

 No current performance issues, but looking at the form library settings, I see this message: 4165 items (list view threshold is 20020). The number of items in this list is approaching the list view threshold, which is 20020 items. This threshold is the limit at which tasks that cause excessive server load (such as those involving all list items) are prohibited.

 I know there is a 5000 limit, but I don't understand the 20k limit? We will be upgrading from 2010 to 2013 soon. Will that help?

 Which brings up the question, when I approach 5000, should I start a new document library for 5001+ ? 

 The list view threshold defaults to 5k. Admins can change it. The fact that you are seeing this message when the list isn't anywhere near the threshold would be a good question to bring up with your SharePoint Admin. More info here. Adding indexes to your list and making sure the default view doesn't return all items can help with performance issues. You may also want to create an archive for older forms - a lot depends on how you are using this info, whether you need access to all items, etc.

 Is there a quick resource I can refer to for archiving?

Not that I know of - you may want to do a web search for ideas. I've seen people take different approaches, like copying forms out of a library when they reach a certain status, or manually creating a new library at the beginning of each year - what works for your process will likely have a lot to do w/ the form, the users, user expectations, etc. :)