Usually they start discussions with the company behind closed doors, because this is cheaper, faster and easier than going public.
But if they don't get their own way they will launch a public campaign, usually starting with a blistering attack on the company's management and strategy.
This is what Elliott Management did with BHP. Talks between the hedge fund and the "highest levels" of BHP management went on for eight months before Elliott went public. Having failed to get its own way, Elliott released a public letter stating that BHP has "underperformed a portfolio of comparable mineral and petroleum companies".
"BHP's management still cannot deliver optimal shareholder value," Elliott said in April, calling for the company to sell its petroleum business, return capital to shareholders and do away with its dual-listed structure, where its shares are listed on share markets in both Australia and London.
It has also launched the FIXING BHP website and came up with what it presumably believes to be a catchy title for its campaign, the "Value Unlock Plan".
When Elliott didn't get the response it wanted, it fired another shot, stating the company's response to its proposals was inadequate.
"Chronic underperformance at BHP means that current management owes shareholders a proper in-depth review and action to optimize shareholder value, rather than running a negative campaign without making its own positive and constructive proposals," Elliott wrote in May.
It's hard not to get the impression that Elliott is casting around for any idea that will stick and could bump up the share price.
Elliott, which in actuality only owns a tiny portion of BHP, is now trying to gather support from other shareholders and could potentially seek a board seat at BHP's annual meetings in October to help prosecute its case for change.
Activist investing by powerful hedge funds is surging in the US, where targeted companies include Apple, Coca-Cola, Dell, eBay, Microsoft, PepsiCo and Procter & Gamble.
According to the annual "SharkWatch" report by US research firm Factset, there were 319 high impact activist campaigns against US companies in 2016. Elliott Management launched ten activist campaigns in 2016, making it the top activist investor by campaign volume.
If shareholder activists get their own way, the shares of the companies they invest in will turn a quick profit as they sell off assets, return capital to shareholders or conduct share buybacks.
But shareholder activism is ultimately to the detriment of a company and its shareholders. Their activism might make a short-term profit but can come at the cost of investments and projects that could underpin long-term profit growth for the company.
This is the risk BHP is facing now.
There are certainly questions around its petroleum assets, particularly the business unit based on extracting oil from shale oil in the US, and around its potash business.
BHP made a long-term US$20 billion (NZ$27b) investment in the shale oil business at the peak of the shale oil boom in 2011. With the collapse of the oil price the business has severely underperformed. BHP is one of the most efficient developers of shale oil in the US. It would be a shame if it sold off that asset and that expertise, only for shareholders to rue the decision when the oil price rises again.
Likewise, BHP's planned potash investment could be a case of bad timing, with potash currently in oversupply. But there are a lot of people in the world who will need feeding, and BHP estimates demand for the fertiliser component will double by 2040.
Maybe selling off these assets is the smart thing to do. But a hedge fund billionaire in New York who wants to turn a quick buck and has no long-term interest in BHP's success shouldn't be driving the decision.
With its decades of experience in resources and deep on-the-ground expertise, BHP is best placed to decide its future.
It would be a great pity for BHP and other companies if it was bullied into giving up on growth investments.
This column has been corrected from its original version, which wrongly said Elliot had "added the sale of BHP's potash business to its list of demands". Elliott has never called for BHP to sell its potash business.