When it comes to cars, there's no doubt about it: Detroit is back. American-brand cars and trucks are better than ever, and sales have been strong.

But this Detroit is different. The companies that used to be known as The Big Three are leaner, sharper, and wiser for the hard experiences of the last decade.

But for all of their recent success here at home, all three are facing big challenges. Here are three of the biggest.

Problem one: Green pressures will force big changes
Ford (NYSE:F) is a huge company, with massive operations around the world. It's Europe's second-biggest automaker, and it's investing a fortune to grow quickly in Asia. But ask any Ford executive about the company's most important product, and they'll tell you without hesitation: pickup trucks.

ImagesThe all-new 2014 Chevy Silverado is GM's most important new product in years. Photo credit: General Motors Co.

You'll get the same answer at General Motors (NYSE:GM), which is starting a huge ad blitz today for its all-new Chevy Silverado, and at Chrysler, too. That's a good thing right now, because pickup sales are booming. But the whole industry is under massive pressure to create products that use less and less gas, and full-sized pickups are very thirsty vehicles. How can Ford and GM and Chrysler continue to make pickups that buyers will like while making the radical improvements in fuel economy that the government is demanding?

For that matter, how will ordinary cars meet the stringent new fuel-economy and emissions rules that will be in place around the world in the next decade? Are electric cars the way forward, as Tesla Motors is trying to demonstrate?

Maybe, maybe not. Right now, Ford is betting on hybrids. And big automakers are teaming up: The Blue Oval has partnered with Toyota (NYSE:TM) to create a hybrid system that will work in its big pickups. Meanwhile, GM just announced that it will work with Honda (NYSE:HMC) to create affordable cars that run on hydrogen fuel cells -- and Toyota, the hybrid leader, says it will launch its first fuel-cell car next year.

And all of those automakers, and most of the rest, are also dabbling in battery-electric cars -- even though batteries remain expensive, heavy, and cumbersome.

How will they solve this puzzle? What will power the cars of the future? Good questions. But one thing's clear: The companies that don't solve it will be in a lot of trouble before long.

Problem two: Big losses and hard times in Europe
Why should American automakers care about Europe? Because they're all losing a lot of money there, that's why. Steep recessions in key European countries have driven new-car sales to a 20-year low. Ford and GM each lost over $1.7 billion in Europe last year, and Chrysler's partner/owner Fiat (NASDAQOTH:FIATY) would be in dire straits if it weren't for Chrysler's recent success here in the U.S.

Euro FiestaFord's Fiesta is oneĀ of Europe's top-selling cars. Photo credit: Ford Motor Co.

All three need the European market, for the scale it adds to their global operations. Ford and GM are pushing ahead with elaborate turnaround plans that aim to get their European operations back to break-even by the end of 2015. And Fiat's CEO is pushing ahead with a plan to merge fully with Chrysler, which will give both companies the scale they need to cut costs and be more competitive around the world.

But in the meantime, Europe is a money pit for all three. Analysts expect new-car sales in Europe to stay low until late in this decade. That means all of the Detroit Three will have to find creative ways to profit in the Old World -- or risk more and bigger losses in years to come.

Problem three: The Japanese government could make it harder to compete
Why should Detroit care about the Japanese government? No, it's not because of Japan's trade barriers, which are actually pretty modest despite what you may have heard. It's because of exchange rates, specifically, because the current Japanese government is trying to jump-start the country's economy by making its currency cheaper.

Who cares? Ford, GM, and Chrysler sure do, and here's why.

When we say the yen is getting cheaper, what we mean is that the exchange rates have moved in such a way that you get more yen for your dollar. Instead of 86 yen for the dollar, as it was at the beginning of the year, now it's around 99 for the dollar.

That means every dollar earned by a Japanese company here in the U.S. is worth more money at home. And that means that the Japanese companies can charge fewer dollars for their products and still have a nice profit when those dollars are converted to yen.

That's a big worry for Detroit. After years of struggling, Detroit has finally reached the point where its best products can compete head-on with the likes of Toyota and Honda, with no excuses (or profit-sucking discounts) needed. Just look at the hot new Ford Fusion, which has been selling like hotcakes -- and gaining on Toyota's Camry in a big way.

ImagesFord's Fusion is going head-to-head with Japan's best -- and winning. Photo credit: Ford Motor Co.

The worry now is that if the yen slips far enough, the Japanese brands will be able to cut their U.S. prices without hurting their profits at home. Nissan already made some price cuts at the beginning of May that gave their sales a big boost.

If the other big names follow suit, then Ford and GM and Chrysler will face a tough choice: Cut their own prices (and profits) to compete, or risk losing a lot of sales. That's why the Japanese government has to be high on Detroit's list of worries right now.

Fool contributor John Rosevear owns shares of Ford and General Motors. Follow him on Twitter at @jrosevear. The Motley Fool recommends Ford, General Motors, and Tesla Motors. The Motley Fool owns shares of Ford and Tesla Motors. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.