The Dow Jones Industrials (^DJI 0.43%) gets so much attention among both investors and the general public because it's the market measure that's easiest to understand. Not only is the math in calculating the average simple, but all the companies in the Dow are also well-known household names that play a role in just about every American's daily life, and investors rarely have to worry about major problems with Dow component companies.

Yesterday, we looked at some of the Dow stocks that are true leaders in their respective fields. But many Dow stocks aren't at the top of their industries and instead are striving to become the kings of the hill. Just because a company isn't the biggest doesn't mean it's not as good an investment, so let's take a closer look at these up-and-coming Dow stocks to see whether they look promising.

Chevron (CVX 1.66%): 1-year return 7.2%, 5-year average annual return 7.8%
Among Big Oil names, Chevron labors in the shadow of much larger ExxonMobil, but Chevron is still a massive company, with operations around the world. In particular, Chevron's liquefied natural gas terminal plans as well as acquisitions of assets both domestically and internationally mark its attempt to become more relevant in an era in which oil majors are seeing falling production.

Just last week, Chevron said it expects much higher earnings when it releases its fourth-quarter report than it posted in the third quarter, with improvements in both upstream exploration and production activities as well as downstream marketing and refining operations. For investors that grew nervous last year with falling oil prices and production levels, Chevron appears to be drilling up success once again.

American Express (AXP 4.66%): 1-year return 26.8%, 5-year average annual return 9%
American Express certainly has a strong marketing presence, but as a card network, it's a distant No. 3 to Visa and MasterCard. Although the company is more widely diversified than its card-network rivals, with a variety of travel-related and other financial services, AmEx still identifies many of its biggest growth opportunities as card-related.

AmEx made a huge move toward broadening its base and becoming more of an industry leader when it released its new Bluebird prepaid card last October. Given AmEx's reputation for aiming at affluent customers, Bluebird opens up a brand-new demographic for the company, as the card targets customers who don't even have bank checking accounts and other traditional banking services. With reasonable fees, the AmEx offering could give the company the chance it needs to connect with new customers and grow its business substantially.

Travelers (TRV 1.49%): 1-year return 28.5%, 5-year average annual return 10.8%
Property and casualty insurers across the industry have labored under the shadow of AIG for years. Even after the near-failure and government bailout of the insurance giant, AIG still has huge amounts of revenue and a bigger market capitalization than Travelers. Still, Travelers has plenty of business, and without the stigma of taking TARP money, the company has a marketable advantage over AIG.

Of course, the ups and downs of the P&C insurance industry will continue to play a big role. Travelers took hits from hurricanes Irene and Sandy, but the stock has nevertheless held up extremely well. Despite near-term catastrophe losses, the long-term impact of higher rates could end up being a net positive for Travelers.

Merck (MRK 0.03%): 1-year return 17.2%, 5-year average annual return (2.2%)
Merck is a drug giant in its own right, but it's still a bit smaller than rival Pfizer. Both drug companies have labored under the same difficulties lately, though, facing big patent cliffs that have forced them to develop new pipelines of promising drug candidates. Moreover, if Pfizer moves ahead with a decision to split itself into component parts, then Merck may inherit the leadership role by default.

In 2013, Merck is hoping to see some successes from multiple prospects that include treatments for osteoporosis, ovarian cancer, and human papillomavirus. Although the company had to pull the plug on its Tredaptive cholesterol drug, rising optimism about Merck's potential could drive investors into the stock even as its rivals choose to break themselves apart.

Will these companies catch up?
These four stocks have generally put up pretty strong performances recently, suggesting that companies with something to prove do their best to push ahead and take over the reins from their rivals. Even though these companies don't yet lead their industries, they have plenty of strong qualities that bode well for their respective futures in the years to come.