Question: Using [PyObjC](http://pyobjc.sourceforge.net/), you can use Python to write Cocoa applications for OS X. Can I write native iPhone apps using Python and if so, how?

Answer: 
Not currently, currently the only languages available to access the iPhone SDK are C/C++, Objective C and Swift.

There is no technical reason why this could not change in the future but I wouldn't hold your breath for this happening in the short term.

That said, Objective-C and Swift really are not too scary...

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**2019 Update:**

While Python-iOS development is relatively immature and likely will prevent (afaik) your app from having native UI and functionality that could be achieved in an Apple-supported development language, Apple now seems to allow embedding Python interpreters in Native Swift/Obj-C apps.

This supports importing Python libraries and running Python scripts (even with supplied command-line arguments) directly from your Native Swift/Obj-C code.

My company is actually wrapping our infrastructure (originally written in Python) in a native iOS application! It works very well and communication between the parts can be easily achieved via a client-server model.

Here is a nice library by Beeware with a cookiecutter template if you want to try and run Python scripts in your iOS app: <https://github.com/beeware/Python-Apple-support/tree/3.6>.