We've now heard from the three biggest players -- Schlumberger (NYSE: SLB), Halliburton (NYSE: HAL), and Baker Hughes (NYSE: BHI) -- in what I consider to be one of the most indispensable sectors for Foolish investors: oil-field services. While there has been an atmosphere of concern about the industry's performance in the first quarter -- based largely on a concerted movement toward liquids-drilling in the U.S., along with shortages of raw materials, I believe the three big amigos have given us plenty of room for optimism about what likely lies ahead for this crucial group.

On that basis, let's briefly recap the companies' performances and attempt to arrive at some overriding themes that might define the sector during the remainder of 2012 and beyond. And while I recognize that Halliburton was the first to report, let's look at them in the order of size.

Schlumberger
Schlumberger reported a 38% spike in earnings, along with a per-share figure after items that jumped year-over-year to $0.98, from $0.71 in the first quarter of 2011. The analysts who follow the company had expected earnings per share of $0.97, so you can term the quarter "in line" or a "beat," depending upon your mood.

In any event, the quarter did little to allay my contention that the big company -- its market cap is more than triple Halliburton's and quadruple that of Baker Hughes -- is the single stock I'd buy if (heaven forbid) I were somehow limited to one name in the sector. Indeed, as long as oil and gas are being produced anywhere on the globe, Schlumberger is certain to be a participant in that activity. That's bound to be the case when a company's complement of employees numbers 110,000 individuals who are plying their trade in about 80 countries.

In North America, the company's revenues dipped by 3.2% as multiclient seismic sales declined sequentially -- a typical phenomenon in the first quarter of most years -- and fracking prices tightened. At the same time, CEO Paul Kibsgaard expressed optimism about increasing activity in the Gulf of Mexico; while Russia, China, and the North Sea softened, albeit seasonally; and activity strengthened in East, West, and North Africa, and in the Middle East.

Each quarter, Schlumberger provides something of a Cook's Tour of its activities and accomplishments by location. By doing so, it puts meat on the bones of its specific functions and provides increased insight into the breadth of its customer base. For the most-recent quarter, the company was busy in such active venues as the Gulf of Mexico, Brazil, Nigeria, Russia, and Saudi Arabia, along with emerging areas like China and the South China Sea.

Halliburton
Despite a hefty $300 million charge related to its role in BP's (NYSE: BP) 2010 Gulf of Mexico disaster aboard Transocean's (NYSE: RIG) Deepwater Horizon rig, Halliburton nevertheless turned in a solid quarter. Indeed, since it was less affected than its peers by the significant switch in the U.S. from dry gas to liquids drilling, the company was able to check in with a nearly 23% year-over-year improvement in its net income.

Perhaps even more impressive was its 40% rise in revenue and 45% jump in operating income in North America, where Schlumberger and Baker Hughes fared less well. No wonder my Foolish colleague Jason Moser recently called Halliburton -- which he believes is "trading at a dirt cheap level" -- his stock of the week.

Baker Hughes
The last of the three biggest oil-field services companies to release its results, Baker Hughes saw its revenues rise by 18% to $5.4 billion -- due in part to a more than 21% increase in North America -- and its per-share earnings of $0.86 top expectations by $0.02.

Nevertheless, CEO Martin Craighead noted that "margins in North America were lower than the fourth quarter due to challenges in the pressure pumping product line, including the rapid transition from natural gas to oil-directed drilling rig activity..." As with his counterparts at the other companies, he also pointed to capacity and pricing pressure in North American fracking.

Internationally, results were strong. Craighead specifically pointed to Baker Hughes having participated in "multiple high-profile wells in Nigeria, Angola, and Mozambique." He also said that the company had landed "high-pressure, high temperature wireline contracts in Europe, and an artificial lift contract for approximately 1,000 wells in Russia."

The Foolish bottom line
Just about five years ago, amid softness in North American activity levels, I noted that Halliburton CEO Dave Lesar had decided to open a second headquarters office in Dubai. Now the primary focus has turned to the technological advancements that have fostered an active market on our continent. It therefore becomes progressively more obvious that there will always be areas of cyclical strength, along with areas of temporary softness in the world of energy.

But given their size and scope, and despite claims that fossil fuels belong to "the last century," Schlumberger, Halliburton, and Baker Hughes will always be where the essential action is, helping to locate and develop the oil and gas that will constitute our core energy sources for decades to come. If you'd like to delve further into the ever-so-important energy picture, I'd suggest you obtain a copy of The Motley Fool's free report, "The Only Energy Stock You'll Ever Need."