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If there is one theme that will be the topic of digital business this year, it is mobile.

ComScore, which tracks Web and mobile usage, published a report about what happened in 2012, and what to expect in 2013.

It shows that the effects of a movement toward mobile are everywhere, from shopping to media to search. According to the report, “2013 could spell a very rocky economic transition,” and businesses will have to scramble to stay ahead of consumers’ changing behavior.

Here are a few interesting tidbits from the 48-page report.

The mobile transition is happening astonishingly quickly. Last year, smartphone penetration crossed 50 percent for the first time, led by Android phones. People spend 63 percent of their time online on desktop computers and 37 percent on mobile devices, including smartphones and tablets, according to comScore.

Just as they compete on computers, Facebook and Google are dominant and at each other’s throats on phones.

Google’s map app for the iPhone, which had been the most used mobile app, lost its No. 1 spot to Facebook after Apple kicked Google’s maps off the iPhone in October. Now, Facebook reaches 76 percent of the smartphone market and accounts for 23 percent of total time spent using apps each month. The next five most used apps are Google’s, which account for 10 percent of time on apps.

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As mobile continues to take share from desktop, some industries have been particularly affected, and they are seeing significant declines in desktop use of their products as a result. They are newspapers, search engines, maps, weather, comparison shopping, directories and instant messenger services.

The most visited Web sites are not so surprising: Google, Yahoo, Microsoft, Facebook and Amazon. Facebook continues to take up most of our time online.

But there were a few surprises from younger, smaller Web companies. Tumblr was No. 8 on the list of sites, ordered by time spent on them. And several Web sites were breakout hits last year, as measured by growth and visitor numbers: Spotify (music), Dropbox (online storage), Etsy (shopping), BuzzFeed (news), JustFab (shopping), SoundCloud (music) and BusinessInsider (news).

Search, one of the biggest and most reliable Web industries, is at a crossroads, comScore said. Even though the search market continues to be extraordinarily profitable, there is a desire for it to evolve and offer new services to users.

Here is some evidence: Searches on traditional search engines, dominated by Google, declined 3 percent last year, and the number of searches per searcher declined 7 percent. Yet searches on specialty sites, known as vertical search engines, like Amazon.com or Whitepages.com, climbed 8 percent.

Social search, based on what users’ friends like, has put Facebook and Google on a “collision course,” comScore said, particularly in searches for local businesses like restaurants.

In social networking, the visual Web, as comScore calls it, has transformed the landscape. Pinterest, Tumblr and Instagram, all of which emphasize images, each gained more than 10 million visitors last year.

Last year was also pivotal for online video, comScore said, as viewers increasingly seek the ability to watch video when and where they want. Watching TV shows online helped last year break viewing records, especially during the Olympics.

In the United States, 75 million people a day watch online video and stream 40 billion videos a month, and viewing is driven by YouTube.

There has also been a turning point for video ads. They cost more than typical ads, and have always lagged behind viewership. But in 2012, 23 percent of videos were accompanied by an ad, up from 14 percent the year before. More TV ad dollars are coming to online video, comScore concluded.

Though e-commerce spending grew 13 percent last year, it was a disappointing holiday season online, largely because of economic pressures. Purchasing on mobile phones is beginning to make a dent in e-commerce, comScore said, with mobile shopping accounting for 11 percent of e-commerce in the fourth quarter of 2012, up from 3 percent in the period two years earlier.