Lumos Labs, who make the brain training app Lumosity have been prosecuted in the US for making unfounded claims. The makers claim that the brain training improves memory and brain function and the website makes strong claims about this.
The FTC (Federal Trade Commission) has previously taken action over another brain training app, plus two others, both for melanoma detection and an app which claimed to improve vision.
Ben Goldacre has weighed in, stating that “Health apps are a giant world of snake oil.”
However, like everything else, there are good and not-so-good apps on the market.
Article here: http://www.statnews.com/2016/01/05/brain-training-lumosity/