Responsive and more - mobile web development with WordPress

Someone said it: "'Would you like to install our app?' is the new 'Skip Intro'"

In the Advanced / Developer meetup for WordPress Austin, we'd like to look at how we can build in mobile-friendly features to a WordPress website in order to try & avoid the need for a separate Mobile App. Mobile Apps have benefits, but the average shelf-life of an app can be less than 30 days. The Web's been around how long? It would seem the better choice, more often than not, would be to use your web presence as your mobile site.

I'd love to hear from people who have done this, obviously, but also those who are experimenting with methods to achieve this. Geolocation, notifications, device UI design features, etc.