Whether you’re using it to saute vegetables or you’re drizzling it on bread sprinkled with sea salt, olive oil should enhance a dish or a snack. Yet many olive oils aren’t particularly good. That’s because bottles on store shelves that aren’t marked with a time stamp can be a blend of old and new oils that taste muddy, waxy or moldy — signs that they’re past their peak, or even rancid.

In a 2012 report on olive oil sold to restaurants and food service sectors, the UC Davis Olive Center at the Robert Mondavi Institute found that some extra-virgin olive oils showed adulteration with canola oil. When tested, some were low on polyphenols, an antioxidant that factors into their health benefits. It’s a sign that the oils were old.

But despite the mysterious origins of some on the market, flavorful, interesting olive oils are just now returning to specialty stores, especially the new-crop olive oils produced in the fall. Whether they come from Greece, Turkey, Spain, Italy or California, they offer a range of characteristics from very mild to surprisingly complex that are tied to blends more than terroir.

Why don’t Americans know how to shop for olive oils? It seems we’ve been more of a butter country.

“America is at level one” when it comes to olive oils, Steven Jenkins told a crowd at last year’s New York International Olive Oil Competition, the largest such event in the world. He’s the olive oil and cheese specialist for New York’s Fairway Markets.

Consumers should look for where an olive oil comes from, the types of olives, the blend and evidence of freshness — either a press date, which should be within the year, or the sell-by date, although most of those are for two years after the olives have been harvested. Olive oil is safe to eat more than a year after it’s harvested, but it’s probably not at its best.

“We should be thinking of olive oil as a food, not as something processed with shelf stabilizers, like Crisco,” said David Lagnese, proprietor of the Wheel & Wedge kiosk at the Strip District’s Pittsburgh Public Market as well as California Olive Oil Connection at the indoor Farmers’ Market Cooperative of East Liberty.

Lagnese is an advocate of domestic olive oils, selling five or six new-crop olive oils from small purveyors. They include the lively, grassy Olio Nuovo Extra Virgin that’s unfiltered and has a shelf life of less than six months as a result. He prices the olive oils so they’re within reach: A 250-milliliter bottle runs $6, 500 milliliters $12 and a 750-milliliter bottle $18.

Lagnese is especially enamored with domestic olive oils partly because the California Olive Oil Council has implemented the most stringent rules for extra-virgin olive oils in the world. The olives need to be handled with care; they can’t be tainted by chemicals, and the oils must be submitted to a laboratory that indicates special handling and storage. It also goes through rigorous taste tests.

Once people incorporate olive oils into everyday cooking, they’ll keep several varieties in the kitchen. But among heavy users, few people use flavored oils. They are frowned upon just as coffee geeks avoid hazelnut-flavored beans.

“The flavoring and the olive oil compete against each other,” said Debra Mortillaro at Dreadnought Wines in Lawrenceville. “If you want a flavor like lemon, use the actual ingredient,” she said.

Over in Lawrenceville at Dreadnought Wines, Mortillaro holds an olive oil class several times a year at the shop, during which she encourages participants to try a range of oils from Italy, Spain, Greece and California. She shows participants how to taste and what to look for when buying olive oils.

Although her passion for wine led her to olive oil, she said the differences surprised her. “I didn’t know what I was tasting or how to assess it,” she said. This led her to a series of classes at the UC Davis Olive Center to learn about olive oil and how olives are harvested.

“When you harvest affects flavor,” said Dan Flynn, executive director of the UC Davis Olive Center. “Olives harvested early lend bitter, pungent and fruity flavor. Late-harvest olives are buttery or nutty.” Each step of the process and how oils are blended play a role in how it tastes.

“The mastery of blending is very important,” Mortillaro said, noting that many olive oils start with a percentage of green olives combined with a percentage of ripe as well as very ripe olives that provide complexity. Once people get the hang of tasting, they better appreciate the blends.

Her favorite olive oils sold at Pennsylvania Macaroni are Frantoia Extra Virgin and Raineri Extra Virgin, both of which are marked with a sell-by date of 2016. The assertive Frantoia is slightly grassy and bitter with a clean finish, while the Raineri is more full-bodied.

Over at Salonika in the Strip District, many customers shopping for olive oils prioritize region. Co-owner Chrysoula Balouris, from Crete, prefers olive oils that she and her husband have imported from her family’s island.

In the back of the shop, a giant green barrel filled with Greek olive oil sits on a pushcart. “This is what every family has in Greece,” said employee Sotiris Aggelous, who has been working at the shop since January.

Although the new-crop Greek olive oils have arrived, the shop is expecting shipments from small farms in Spain and Turkey — farms the Balourises visit every year.

Customers can serve themselves from the stainless steel vats that were just cleaned and filled with the new shipment. Bigger-name brands have also arrived and align beside the vats, in 3-liter tins from Crete and Kalamata. The 2016 sell-by dates are marked on the top of the tins.

“This would last my family a week,” Mr. Aggelous said, pointing to them.

His family uses olive oil in ways that defy conventional wisdom in the U.S. “Americans think you can’t fry with olive oil, but tell my mother that,” he said.

When his mother needed olive oil, she would go down to the barrel in the cellar, lean over it and fill a glass bottle to bring to the kitchen. His family would go through the barrel before the year was through.

“When my mother said, ‘I cannot reach,’ it meant we were low on olive oil,” he said. They’d visit a local farm, where they’d bring back five or six tins to replenish the barrel.

Although such prolific use of olive oil isn’t the norm here, he believes once people taste the good stuff, olive oils will come into more widespread use.

“Or at least,” he said, “that’s the goal.”