It was in 1896 that Charles Dow, co-founder of Dow Jones & Company, created the index that still bears his name.

Today, indexes such as the Dow Jones industrial average and the S&P 500 (for shares listed in New York), or the FTSE 100 (for London), are among the best-known brands in financial markets. The role they play has expanded massively in recent years.

Index makers have become finance's new kingmakers: arbiters of how investors should allocate their money.

Stock market indexes were devised as a measure of the overall market, against which those trading in shares could compare their performance. At first they were concocted by the press or by exchanges themselves. For bonds, indexes were compiled by the banks that traded them. Except for a few of the very earliest indexes, such as the Dow, which is weighted by share price, nearly all are weighted by market capitalization or, in the case of bond indexes, by the volume of debt outstanding.

Three large firms — FTSE Russell, MSCI and S&P Dow Jones Indices — dominate equity index making. The amounts of money they influence are staggering.

S&P Dow Jones reckons $4.2 trillion in assets are invested in "passive" funds that track its indexes, with $3 trillion assigned just to the S&P 500. Another $7.5 trillion in actively managed assets use its indexes as "benchmarks": that is, they measure their performance against them.

The two other big index providers command similarly vast sums: $15 trillion in active and passive money follows FTSE Russell's indexes, and $11 trillion hug MSCI's.

Index makers insist they are less powerful than they look. Alex Matturri, head of S&P Dow Jones, pointed out that even though assets in exchange traded funds (ETFs), virtually all of which are passive, have reached $4 trillion globally, that is only a "small part of the global investable universe" of around $300 trillion. Matturri also emphasized the transparency and "rules-driven approach" of index construction and governance. Big changes are made only after consulting the market.

Moreover, argued Mark Makepeace, chief executive of FTSE Russell, index making remains very competitive. Some smaller providers, such as Morningstar, give away data on most of their indexes (on the weightings of their components, for example). They charge a fee only if a passive fund wants to track an index and use their brand. The big three charge both for access to data and for the use of their indexes in passive funds.

Regulation also constrains the firms. From January 2018, index makers in Europe will be directly regulated under the E.U.'s "Benchmarks Regulation," which includes requirements such as an annual external audit for benchmarks deemed "critical," and direct oversight by the E.U. regulator.

Nevertheless, index makers' power is considerable. It is boosted by the rise of passive investing. In the U.S., for instance, three-tenths of assets are now in passive funds. And though some smaller competitors survive, the index industry is becoming more concentrated. Many banks have quit the bond-index business. Bloomberg acquired Barclays' indexes last year; FTSE Russell has nearly completed the purchase of Citigroup's.

Despite harping on the objectivity and transparency of their rules, moreover, many of the decisions that index providers make are, ultimately, subjective. Take the decision in June by MSCI to include Chinese shares in its emerging-markets equity index (followed by around $1.6 trillion in assets).

Shares listed in mainland China had been excluded because of the opacity of China's capital markets, and the restrictions foreigners face there. China's capital controls remain in place, but, after consulting market participants, MSCI decided to include the shares — albeit at a weighting.

Similarly, both FTSE Russell and S&P, in the wake of Snap's listing on the New York Stock Exchange in March, chose to alter their rules to exclude companies that list only nonvoting shares (as the tech firm did).

For as long as indexes have acted as shorthand for the markets they seek to capture, index makers have received attention. Their importance has grown to match their profile. Being the source of "authoritative guidance" on what should even count as an asset class brings new responsibilities. Index makers will have to get used to ever more scrutiny.