Founder of Airtable here--Airtable is actually a relational database with foreign key relationships (the technicalities of which are abstracted away from the user). It's designed specifically to be somewhere between the accessibility of a spreadsheet and the customizability/structure of a Filemaker/Access/Force.com, all with a much more modern UX and collaboration experience. Airtable.com/product or Airtable.com/templates offers some more context!
Thank you for Airtable, I'm a big fan, especially of the Zapier integration. Lately there has been a lot of discussion on Hacker News about projects like Opps Daily [1] and Nugget [2], where people write in about some pain point they have in their daily job that might be solved by custom-built software. I get the impression that Airtable + Zapier could solve a lot of those use cases.
Airtable looks like exactly what the world needs for a modern system to let everyday users manage data well rather than bunging it all in a spreadsheet.
But the row limits are too low for many obvious uses. I assume this is for technical reasons? Otherwise it doesn't make much sense that if you pay for 20 users to share a database you get the same number of rows as if you pay for two.
1) Foreign keys to users (for e.g. "assigned to", "team members")
2) Better programmability - right now, anything moderately complex requires a bunch of intermediate column (that then have to be hidden from all views). Objective spreadsheets (MIT SAIL) seems like something to aim for.
3) Programmatic (API) access to row history - at least read, for reports