Mozilla's team has been working on an application for the iPhone based on the Firefox Sync (formerly Weave Sync) technology. The app is called Firefox Home, and it gives iPhone users instant access to their Firefox browsing history, bookmarks and the set of tabs from their most recent browser session. What’s more, it provides Firefox "Awesome Bar" capability that enables people to get to their favorite web sites with minimal typing.

Firefox Home encrypted end-to-end.

Users will be able to access to the list of tabs they just had open on their desktop via their iPhone. Need those directions to that restaurant you were just reading about on your desktop? The confirmation code for your flight? Just start typing in the Awesome Bar and those pages will be right at your fingertips.

The project information is here: https://wiki.mozilla.org/Mobile/firefoxhome