Mobile phones, wearable devices and self-driving cars are generating buzz as the future of technology. But the old Web browser is being reinvented too, in a trend with implications for how consumers work and entertain themselves online.

Companies from Google Inc. GOOG -0.31% to small startups are introducing new features, such as taking and syncing notes and files within the browser, voice-recognition, video calls and messaging. They are also reinventing the browser for newly connected devices like cars.

In one new front of experimentation, browser company Maxthon Ltd. will next month offer users the ability to sync downloads and local files across devices via its browser, in potentialcompetition with file-sharing services like Dropbox Inc. Consumers will be able to download or send the data to a cloud storageaccount or other devicerunning the browser from a drop-down menu within the browser. The company already offers the ability to take and sync notes in the browser.

The little-known software, which Maxthon says has some 120 million monthly users, more than half of them in China, aims to capitalize on consumers' desires to access their files from a range of devices. The company offers browsers for desktops, mobile phones, tablets and even in-car systems. Earlier this year, Maxthon announced a deal with Pioneer Electronics to enable users to browse the Web from an in-car touch-screen device.

'It's clear we're shifting to a multi-device world and that creates a lot of pain points,' says Karl Mattson, vice president and general manager of Maxthon, which has about 220 employees. 'The browser is the natural frame for this,' he says.

The browser industry may have appeared staid in recent years, with the market dominated by tech giants such as Microsoft Corp., MSFT +1.04% Google and Apple Inc. AAPL +0.39% Microsoft's Internet Explorer remains the market-share leader for desktop browsers, according to Net Applications, with a 56% share of the desktop market globally. Apple's Safari browser leads on mobile phones and tablets, with 59% share, thanks to the popularity of the iPhone and iPad.

But behind the scenes, many companies have quietly been enhancing and reimagining the Web browser, as new technologies have made it possible to do numerous activities in the browser instead of through software downloaded to a computer or mobile device. The set of new programming techniques enabling the features is often referred to as HTML5.

Companies have opened up to 'add-ons' and apps, allowing users to access features like games and third-party software from a homescreen. Earlier this year, Google, which develops the Chrome browser, released software that allows developers to add voice-recognition to their Web pages, so users can browse the Web by speaking. It also released a Chrome app for its Google Keep note-taking service that syncs notes directly with its Google Drive storage service.

Microsoft has been tailoring its Internet Explorer browser for touch, focusing on making it responsive and fast for tablets like its Surface. The latest version of Internet Explorer also is designed to work well with its SkyDrive storage service.

Apps have stolen some thunder from browsers, especially as consumers find apps faster and more convenient to use than the Web. That has spurred some of the latest browser innovation.

Jay Sullivan, chief operating officer of browser maker Mozilla Corp., says browsing is going to become more social through new and easy ways to share what people are browsing with friends. 'It will be more lively, quick and fun,' he says.

Mozilla's Firefox browser has rolled out new features, such as the ability to integrate with social-networking sites so users can see updates and messages from Facebook Inc. FB +0.52% within the browser's frame. It is also testing the feature with Sina Corp.'s SINA -0.76% Weibo for Chinese users.

Mozilla also is working on embedded communication features. For instance, consumers could open up a chat screen within their browser and drag a video from a Web page into the screen to share immediately. Mozilla is also trying to persuade websites to adopt a new identitysystem called Persona that aims to eliminate passwords. It allows users to log into websites using existing accounts and passwords.

Past attempts to spiff up browsers haven't always taken off. Onetime Web-browser startup Rockmelt, which once trumpeted its integration with Facebook, says its desktop browser had 4.5 million users but will be discontinued in the next few months. It has changed course to become a discovery service for finding interesting Web content.

Tim Howes, Rockmelt co-founder and chief technology officer, said in a statement that 'browsers today are just big dumb windows in [consumers'] way.'

Some new browser features, like file-sharing, aim to replicate functions or Web services that are already easy to access across multiple devices through services like Google Drive or Dropbox.

Mr. Mattson of Maxthon says integrated features are more convenient for users. He likens some of the stand-alone services to 'using a five-pound hammer to kill a mosquito' when something simpler within the browser will do.