Tom Brady, Venus Williams, Penélope Cruz, and Rosie Huntington-Whiteley have something in common, aside from being unnaturally beautiful: They’ve all followed forms of anti-inflammatory (AI) diets at one time or another. Tom has done it to boost his performance on the football field. Venus said she did it to help keep her autoimmune disorder in check. And Penélope and Rosie have followed an AI-style detox to keep their skin radiant.

These celeb diets may be buzzy, but the tenets of an AI diet—more plants, less sugar, no refined stuff—are far from a passing fad. “Who needs to eat a more anti-inflammatory diet? Everyone,” says Barry Sears, PhD, creator of The Zone diet, who has spent decades studying chronic inflammation. Here’s the lowdown on inflammation—and how to fight it with food.

What the heck is inflammation, anyway?

Believe it or not, inflammation starts as a good thing. It happens when your immune system sends out white blood cells and “warrior” compounds like eicosanoids to attack invading viruses, bacteria, or toxins. A classic example of totally normal inflammation: pain, heat, redness, and swelling around a wound or injury (think of a tender sprained ankle).

“There’s a separate response called ‘resolution’ that brings the dogs of war back to their barracks and heals your tissues,” says Sears. “The first phase of inflammation causes cellular destruction, and the second phase, resolution, begins cellular rejuvenation. As long as those phases are balanced, you stay well.”

But for more and more of us, the balance never happens. That’s because sugar, refined grains, and saturated fat can also trigger an inflammatory immune response, notes Sears, and the typical Western diet is packed with them, meaning we’re inflaming our bodies over and over, every time we eat. Meanwhile, guess what the average American gets way too little of: fruits and non-starchy veggies, which are packed with antioxidants that help cool things down and reduce the intensity of the initial inflammatory response, and fatty fish, a great source of omega-3 fatty acids, which can help move your body into the resolution phase.

Air pollution and environmental toxins also trigger your immune system this way, but “most of the chronic, extra inflammation in our bodies is diet-related,” says Sears. In arteries, chronic inflammation can lead to heart disease. In the brain, it’s linked to anxiety and depression. In your joints, it causes swelling and pain. In the gut, inflammation throws off the balance of helpful bacteria and causes direct damage to the lining of the intestines, says Mark Hyman, MD, director of the Center for Functional Medicine at the Cleveland Clinic and author of The Blood Sugar Solution: 10-Day Detox Diet. That may contribute to IBS, food sensitivities, autoimmune diseases, and even obesity, research suggests.

In contrast, research shows that following a more anti-inflammatory style of eating may reduce the risk of heart disease, obesity, and some cancers and may even extend your life, says Frank Hu, MD, professor of nutrition and epidemiology at the Harvard T.H. Chan School of Public Health. Other claims about anti-inflammatory diets—for example, that they can reverse autoimmune disease (the goal of the Autoimmune Protocol, an extremely restrictive AI diet) or improve mental health—have less solid proof, he says.

 How to spot an anti-inflammatory diet

There isn’t just one specific “AI Diet,” unlike Atkins or South Beach. Sears’s Zone diet and Dr. Hyman’s Detox are both highly anti-inflammatory, as is the soy-heavy plan that integrative medicine guru Andrew Weil, MD, offers for free on his website. Paleo and Whole30 diets are both AI, too.

But the plan with the most research-backed anti-inflammatory cred is the traditional Mediterranean diet, emphasizing fruits, vegetables, whole grains, legumes, fish, and olive oil. Several very large studies—including the famed Nurses’ Health Study—have found that people who follow a Mediterranean pattern of eating have lower levels of the inflammatory markers C-reactive protein and interleukin-6 in their blood compared with those who don’t. This may be one reason the Mediterranean diet is linked to so many health benefits, from keeping weight down to slashing heart and stroke risk, notes Dr. Hu.

The goals of an AI plan are simple: Cut way back on foods that trigger an inflammatory response and eat more of the foods that heal damage. While there are some variations in what’s allowed and what isn’t, most AI plans share an emphasis on eating whole, minimally processed foods, non-starchy vegetables, monounsaturated fats like olive oil and avocado, colorful berries and other fruit, and lots of omega-3s from fatty fish (or supplements), and avoiding added sugar and refined grains.

That said, your plate might look a little different from your friend’s or coworker’s, and that’s the way it should be, says Dr. Hyman. Some people thrive on a grain-free Paleo plan, while others would rather die than give up bread. Food sensitivities play a role, too: “People react to foods differently, and if someone has a sensitivity to a particular food, it will lead to cytokine production and an increase in other inflammatory chemicals,” says Dr. Hyman. (If you suspect you have a sensitivity, talk to your doctor or a dietitian, who can design an elimination diet to help ID the culprit.)