Which language learning app is most strongly based in the latest science of language acquisition?
I feel there is no one app that is available today that will take care of language acquisition.
Spaced repetition software focuses on repetition just before/as somebody is forgetting. Apps like Memrise and Anki are good for this.
However most studies in language acquisition have shown that hands on comprehension and production of the language in novel situations is probably best.
There is yet to be an app that replicates this but the apps that are available on the market today are useful supplementary aides.
Have a look at Language Immersion Online | Learn a Language with Videos | FluentU or LingQ for some interesting input based CALL (computer assisted language learning). I feel spending time with programs like these which deal with natural language as spoken by native speakers will give you a much better foundation than the apps that are available so far.
Personally I learn best with a personal instructor or study partner. Having a few hours a week with them is usually enough to keep me progressing in the language. I then review the sessions outside class to give me some extra repetition. This makes the input more meaningful for me too, which I think is important.
Looking forward to reading everybody else's thoughts.