I'm incredibly late to the party on local site development. The tools have been around for a long time but I've never got on board until now.
So given the popularity of MAMP and the proliferation of mobile devices I assumed there had to be some simple way to test your locally hosted sites on mobile devices.
I'd googled the same question a dozen different ways until coming across the answer. You'll find plenty of blog posts advising you to install extra software to work in conjunction with MAMP, or to start messing around with proxies and what-not.
This is much simpler.
The answer is Forward
Forward simply creates a 'tunnel' from your localhost through to a unique URL. You then use that URL on your mobile devices. That's it!
Once you've got a Forward account, open the site running on your MAMP server. With one click of the Chrome Extension you setup a URL that anyone in the world can use to view your locally hosted site.
So not only is it great for local development, but it allows you to share your local version with clients as well.
It works for static sites and even those running on a CMS. It's perfect for WordPress actually. With most of the other solutions I found for viewing locally hosted sites the Site URL would always break. Forward has created a plugin to solve this, all you need to do is install it, activate it, and your WordPress site works perfectly.
If you're new to local development or looking for a better way to develop and test local sites on mobile it can't get much easier than this.
In five minutes I went from having no solution to this problem, to developing and testing sites on mobile.
A note on MAMP Pro
As of writing this I'm using the free version of MAMP. Unfortunately this places all the sites I'm locally developing in the one folder, meaning anyone I sent the link to could view every site on the host.
The solution would be to use MAMP Pro and create a different local host for each site. So MAMP Pro would be a good idea if you're developing multiple sites.