People are certainly buying the hype—and the games. According to one set of estimates, consumers spent $715 million on these games in 2013, and are set to spend $3.38 billion by 2020.

And they might be wasting their money, according to a team of seven psychologists led by Daniel Simons at the University of Illinois. The team, most of whom have worked on brain-training themselves but have not received money from the industry, spent two years reviewing every single scientific paper cited by leading brain-training companies in support their products—374 in total.

Their review was published today, and it makes for stark reading. The studies, they concluded, suffer from a litany of important weaknesses, and provide little or no evidence that the games improve anything other than the specific tasks being trained. People get better at playing the games, but there are no convincing signs that those improvements transfer to general mental skills or to everyday life. “If you want to remember which drugs you have to take, or your schedule for the day, you’re better off training those instead,” says Simons.

“The review really leaves nothing out—and the evidence is unimpressive,” says Ulrich Mayr from the University of Oregon, who studies mental flexibility. “Seeing it so clearly is a service for the whole field.” Michael Kane from the University of North Carolina in Greensboro, who studies attention and memory, agrees. “It’s a tour de force,” he says. “It’s exceedingly fair, and a model of what a skeptical but open-minded evaluation of evidence should look like.” (Both Mayr and Kane recently signed a consensus statement from 70 psychologists and neuroscientists disputing the “frequently exaggerated and at times misleading” claims around brain-training games.)

Open-minded? Hardly, says Henry Mahncke, a neuroscientist and CEO of Posit Science, who accuses Simons’s team of being biased and inaccurate. “They twisted every one of those studies to fit their theories that cognitive training can’t work,” he says. “This is what happens when one paradigm topples another. It’s like [the authors] locked themselves in a cell for the last 100 years and talk about a style of psychology uncontaminated by neuroscience.” Brain-training, he asserts, isn’t a magic bullet, but does indeed generalize to important real-world tasks. To say otherwise is “completely wrong.”

Others in the field are more sanguine. “The evidence could be stronger,” says George Rebok from John Hopkins Bloomberg School of Public Health, who took part in one of the best brain-training studies around. “The review is very timely, and will help us raise the bar on the science of brain-training.” Similarly, Erica Perng, director of communications for Lumos Labs, sent a statement saying: “We strongly believe in the value of cognitive training. Our hope is that this debate enables more researchers to produce high-quality, replicable results that will move both the industry and scientific community forward.”