In Yahoo’s (YHOO) case, Daniel Loeb, founder and CEO of hedge fund Third Point LLC — the company that owns a 5.8 % stake in Yahoo — is threatening a proxy fight after Yahoo recently decided to keep him off the board. Yahoo appointed three new members, and it seems to be holding to its decision to turn the company around under the leadership of CEO Scott Thompson, appointed six months ago. Part of that plan will include laying off staff members, possibly thousands of them, starting this week.

Loeb could either convince the board to bend to his will or he can take his investment money and bail. But the role he’s playing, that of activist investor, has grown more influential in the corporate world over the past decade, taking up a larger piece of the CEO-board-shareholder triumvirate.

“Since 2000, it seems that companies are really worried about hedge fund activism,” says Yaniv Grinstein, an associate professor of finance at Cornell’s Johnson School of Management. “They take it more seriously than they used to.”

That’s because activist shareholders generally make major changes at companies. In a paper published in 2009, NYU Stern School of Business professor April Klein looked at 151 activist hedge fund targets between 2003 and 2005. She found that out of those 151 targets, activist shareholders received a seat on the board about 44% of the time. Once there, she says, they “really did shake things up dramatically,” pushing for new CEOs or major overhauls.

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Surprisingly, Klein adds, these shareholders generally don’t own a majority stake in the company, sometimes as little as 2%. “To me, that indicates that they were not the only people that felt that something could be changed,” Klein says.

Yet the jury’s still out about whether that power shift is ultimately good for companies. It certainly seems to benefit shareholders, Klein says, though not necessarily bondholders. After increased investment from activist shareholders, she says, “Companies were selling off assets and doing a lot of restructuring, so bondholders had less cash, fewer assets, and more debt.” The evidence is inconclusive about whether, on the whole, activist shareholders who get on the board boost overall profit at companies.

The power struggle between management and activist investors can certainly grow ugly. “Most CEOs have pretty big egos, as do most of these activists investors,” says James Shein, a management professor at Northwestern’s Kellogg school of management. “I liken them to two sumo wrestlers trying to knock each other out of the ring.”

Several companies have been able to muddle through messy, yet arguably beneficial, battles with activist investors. In 2007, Relational Investors LLC, a hedge fund headed by Ralph Whitworth and David Batchelder, threatened a proxy fight at Home Depot (HD). The company backed down, and ultimately appointed them to the board, where they successfully pushed for replacing then-CEO Robert Nardelli with Frank Blake. Since 2007, Home Depot’s stock price has increased by over 30%.

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More recently, J.C. Penney (JCP) had a back-and-forth with activist investor William Ackman of Pershing Square Capital Management. In October 2010, Ackman announced that he would buy a 16.5% stake in J.C. Penney. The company then tried to prevent a takeover by enacting a shareholder rights agreement, or poison pill, that would devalue the stock should any one shareholder buy more than 10% of it. Since Ackman already owned over 10%, the poison pill would kick in if he bought any additional shares.

But Ackman held his ground and was appointed to J.C. Penney’s board in 2011, where he pushed for former Apple (AAPL) executive Ron Johnson to take over as CEO of the company (Johnson officially took the reins in November 2011). Since the beginning of October 2011, J.C. Penney’s stock price, like Home Depot’s, has increased over 30%.

To be sure, these proxy fights can be incredibly distracting for a company, says Shein, who has been on the board of a company during one. But they are in place for a good reason, he says: “If you have a CEO whose ego is controlling everything and you have a board that won’t override or even question it, that warrants a proxy fight.”

As far as Yahoo’s situation goes, “the board needs to communicate clearly what they’re up to and try to stick to the strategy,” Grinstein says. This is true for management everywhere, because now, more than ever, activist shareholders are waiting in the wings.