(FORTUNE Magazine) - I'm delighted to inform you that the board has unanimously chosen you to be Microsoft's new chairman and CEO. Now that Messrs. Gates and Ballmer have unexpectedly retired to Fiji, the board is counting on you to lead the company forward--from a business based on virtually controlling the world's personal computers and selling software at astronomical profit margins into a completely different business where the rulers of the Net increasingly control our company's world and a lot of competing software is free. Congratulations! You start Monday.

Now: Do you have the remotest idea of what you're going to do?

Welcome to the world of tough jobs. Not ordinarily tough, but monumentally, head-swimmingly tough. Rick Wagoner at GM may have the toughest of them all (see the preceding article), though billionaire investor Eddie Lampert has put himself in contention by trying to revive not one but two of America's most troubled retailers, Kmart and Sears (see the story on page 90). On the following pages we've assembled ten more killer jobs and their current holders (including Mr. Ballmer, who has not, in fact, retired to Fiji). These tough jobs don't involve crises; unlike GM, each of the ten companies is still highly profitable. Yet all face profound issues that signal some of the most important trends in the economic world--and because the stocks of the companies are all widely held, their course has huge implications for the financial markets.

Are today's toughest jobs really any more demanding than yesterday's? After all, people like to believe they live in the most challenging times ever, but isn't that just egotism? In fact, strong evidence says the hardest jobs now really may be in a class by themselves. That's because the world economy is going through a genuine epochal transformation on the scale of the industrial revolution 200 years ago. As we move toward an information-based economy in which computing power, data storage, and telecommunications are virtually free, the challenges are fundamentally different and deeply unfamiliar. The toughest jobs are the ones you don't know how to do, and in this new economy those are mostly the jobs we face.

Exhibit A: The Moving Model The class of problem that's arguably hardest to fix--and most emblematic of the changing economy--is the outmoded business model. Among the companies on our list, Microsoft, Sony, Verizon, Wal-Mart, and perhaps others face that challenge. Time was when a company could turn the crank on a good business model for decades; think of Kodak, Sears, Xerox, or any other icon of 20th-century commerce. No more. Former Xerox CEO Paul Allaire spoke for millions of managers in 2000 when he famously told a conference call of Wall Street analysts: "We have an unsustainable business model." That's a sentence every CEO should put on a laminated card and carry in his pocket.

In an information-based economy, untethered to physical assets, business models can and will change continually. Yet for most companies, changing them is almost unbearably difficult--think again of Kodak, Sears, and Xerox. Arguably the champ at adaptation is Intel. Its recent shift away from PC chips is at least its fifth major change in business model. Those kinds of changes terrify most executives, but if Intel hadn't made them, CEO Paul Otellini would today be in one of our ten toughest jobs--or more likely, the company would be dead.

Exhibit B: The Power Players The economic revolution is making the hardest jobs harder in another way, by changing the relationships between corporate chiefs and the other players in the game of business--almost always to the chiefs' disadvantage. Most important, customers have more power. Partly that's because they have more information; in the Internet Age they know what everything costs and how much you're charging in every market. Then add global overcapacity in almost every industry, which increasingly forces you to compete on price. Customers rule; suppliers grovel.

There's more: Investors are more powerful than ever, since they're more likely to be big institutions rather than individuals. Boards of directors are more powerful, prodded into their new role by scandals. Highly skilled employees are more powerful, with talent becoming the new critical production factor just as the largest-ever army of workers, the boomers, begins leaving the workforce.

Add it all up, and CEOs are facing some of the hardest problems ever from a position of less relative power than they've held in generations. Could it get any tougher? Actually, it could. Because sometimes a CEO (like Coke's Neville Isdell) lands in one of these jobs after a predecessor or two or three has failed at it, letting problems get worse before moving on. That kind of situation has always been with us and always will be, which is no consolation to those who are in it.

The Upshot: Comebacks and Collapses Some of these jobs will prove too tough, and the companies involved will become sad stories of decline. The great opportunity for investors is distinguishing those from the wonderful comebacks waiting to happen. A list of toughest jobs in the '90s would have included those of Lou Gerstner and Larry Bossidy, newly arrived at IBM and AlliedSignal (now Honeywell), and that of Steve Jobs, newly returned to Apple Computer. You could have argued plausibly that all three situations were hopeless, but of course those jobs got done masterfully, producing spectacular rewards for investors. You'll read our investing calls on all ten companies we discuss.

The best thing about CEOs on the spot is that they're responding to the biggest problems of a revolutionized economy, showing the way for the next generation of business leaders. Cheer them on and learn from them. We can even be inspired by them to adopt a new attitude. Instead of dreading daunting challenges, let's embrace them. The U.S. Navy SEALs have a favorite saying: "The only easy day was yesterday." In today's economy, that belongs on the laminated card too.

FEEDBACK gcolvin@fortunemail.com

The New Deal

It always seems as if life was easier in the past. But for many corporate chiefs, it really was: Today crises come faster, and customers, boards, and investors are more powerful.

Yesterday's Headaches

Sourcing, making, and marketing goods in a manufacturing-based economy

Trying to amass market power in commodity businesses

Negotiating with unions

Fighting domestic competition

For big companies (AT&T, GM, IBM): keeping market share down to avoid antitrust problems

Today's Headaches

Continually altering business models in an information-based economy

Confronting increased customer power and investor power in all businesses

Attracting and keeping top talent

Fighting global competition

For all companies (including the biggest): finding profitable growth in a world of overcapacity