When I first started out, I treated my database as just a dumb datastore. Thankfully my database was Postgres (a decision made by the team I got a job with, who obviously were much smarter than me). I think most programmers start out this way, probably because they learn a procedural language (PHP, Python, Perl) before SQL. So it's easier to write their application rules there.

Regardless, even when I was using Postgres as a dumb store, I was still using it to enforce uniqueness --- which is otherwise very hard to do anywhere else. Later I started to add foreign-key constraints (I know!). Slowly I found out that other things, like eligibility checking, complex calculations, and other processing, were always much shorter in SQL than in my procedural language (which had to pull the data from the database anyway to work on it). And all other things being equal, my criterion for how to do something is, "Which way is shorter?" That's usually also the fastest to run and the easiest to maintain (though I'm not talking about using one-letter names for variables and functions --- at least not always ;).

Now I'm slowly moving toward my middle language (PHP) being little more than a templating language. I think I heard that Oracle had even moved HTML formatting to the database in one of their products, but that's going a little too far.