How does Airdrop work under the hood I have an iPhone 5s (iOS8.4) and an MBP 2012 (10.10.4). I had this problem since Apple introduced Airdrop.

I set bot the MBP and iPhone Airdrop to "everyone". MBP sees the phone and can send all sorts of files.  The phone receives them fine, it prompts then I say yes.  The other way it does not work. The iPhone does not see the MBP. However, if I try hard enough, (including hard resets) it ends up working.

Now iPhone 5s - iPad mini 2nd generation work like a charm, both ways, and so does iPad mini 2nd generation - MBP.

My questions are


Is this expected? Does iPhone 5s have partial Airdrop support? 
In general, how does Airdrop work under the hood?  Bluetooth? Ad-hoc wifi? Does it make a difference if the devices are on the same wifi network?
iPhone 5s has full AirDrop support, so the problem you're describing is strange, and something I don't have an explanation for. 
AirDrop for iOS uses both Wi-Fi (Direct) and Bluetooth technologies. AirDrop for OS X uses Wi-Fi (Direct) only.