The Mozilla Foundation put out Firefox 3.5 this morning—the latest version of its blockbuster browser, which has steadily chipped away at Microsoft’s lead, although it still only commands about a quarter of the browser market in the U.S.

For all Mozilla’s progress, a big challenge remains reminding users that they have a choice beyond Internet Explorer which is likely pre-installed on their computers. In addition to the 800-pound gorilla, there are newer players in the market too, like Apple’s Safari and Google’s Chrome. Indeed, the Firefox development cycle has sped up in part due to these entrants.

The updated browser looks basically the same as Firefox 3.0, which came out a year ago. But the company says 3.5 is speedier and also comes with a number of new features, including a private browsing mode.

We chatted with Firefox director Mike Beltzner earlier this month about the state of the browser. Highlights from the conversation, including Mozilla’s relationship with Google (NSDQ: GOOG) and ways the foundation may change Firefox’s user inferface in the future:

—Beltzner says Mozilla’s relationship with Google hasn’t changed since Google introduced its own browser, Chrome, last fall. Mozilla depends on Google for most of its revenue, since Google pays to have its search engine be the default in Firefox. “They were at our office two days ago so we could all talk about some of the technology they put into Chrome,” Beltzner says. He says the common target for both browsers remains Microsoft (NSDQ: MSFT), which recently introduced a new version of Internet Explorer: “Fundamentally, I’d rather have people using one of the modern browsers than not.” He adds that since the launch of Chrome, the growth in Firefox’s market share has only accelerated. “The majority of the web audience today (still) does not understand there is a choice in terms of the web browser (they use),” he says.

—Next up for Firefox will likely be a revamped user interface. Beltzner says that some of the things that Mozilla is looking at are ways to improve the staid menus and taskbars on top of the browser. “My biggest pet peeve with all web browsers is the location bar—after you’ve gone to a website it just sits there and gives you pretty useless information—that space across the top could be much more dynamic and much more interesting,” he says. Beltzner says it’s possible that a new version of Firefox could have those controls fade into a loaded web page, so that it would not occupy much space but a user could still click on it if he or she wanted to access it. He also says there is room to make browsers smarter, considering the amount of data they can collect on a user’s habits. “It can tell that if I go to Apple.com/trailers, 90 percent of the time the next site I go to is comingsoon.net to look at the trailers there,” he says. “The browser can start to do pretty clever things ... predicting where you want to go to next and recommending perhaps where you may may want to go to next.”

—Plans are in the works to get Firefox on to more mobile phones. Currently, there’s an alpha version for Windows Mobile and a beta for some Nokia (NYSE: NOK) phones—but that’s it. Beltzner hopes to be shipping a mobile Firefox version by the end of the year. “The mobile space is still not very open,” he says. “There are devices like the iPhone, like Andorid devices which are more open than smartphones used to be but they’re still not open enough that any software vendor can compile software and have it installed on the phone.”

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