Do you exfoliate before or after shaving?

I've Googled this many times and there are a lot of discussions out there on this topic.  Some exfoliate after because exfoliating before shaving can irritate the skin.  Some don’t do it at all because shaving already abrades layers of dead skin.

Personally, I subscribe to the philosophy of exfoliating before shaving.  I find that a gentle exfoliator doesn’t irritate my face (or head) before a shave and it leaves my stubble a little more exposed and allows the blade to shave closer to the surface. Exfoliating afterwards leaves my face feeling raw … like how your nose may feel when you've got a cold and you’re constantly rubbing tissues against it.

Pictured (From Left): Unnamed coarse one, Every Man Jack Signature Mint Face Scrub, Game Day Men's Pre-Shave

I've tried a number of exfoliators and some have simply been too coarse. But there are others like the Every Man Jack Face Scrub or the GameDay Men’s Pre-Shave that the granules feel finer and gentler.  

I suppose everyone is different and needs to find what kind of exfoliator and whether to exfoliate, before, after, or at all works for them.  

So … do you exfoliate before you shave, after, or at all?  We’d love to hear about it.