Ever since I taught myself some Latin with Ørberg's Lingua Latina per se illustrata when I was 18, I've been fascinated with learning languages exclusively in the target language, that is, without translations and explanations in your native language. Ørberg's course is entirely in Latin and it's far from being the only one of its kind. Unfortunately, after a period of popularity starting at the end of the 19th century, textbooks that teach languages following this so-called direct or natural method seem to have fallen out of fashion in the 1960s. So most of the available direct-method textbooks for modern languages today are hopelessly outdated if you study for communicating with native speakers. However, if you are interested in reading classic literature, these books are still great.
Two sources of high-quality books following the direct method have been Worman's Modern Language Series and the courses published by the Nature Method Institute, including Ørberg's Latin course. Some of those are very difficult to get your hands on (for example, the Russian textbook by the Nature Method Institute), but many have been digitized and can be downloaded (check this list). Yesterday I found out that a Turkish institution started to publish videos on Youtube with chapters from some of these books recorded by native speakers, so you may even study with audio.
I hope that direct-method textbooks with monolingual explanations and helpful illustrations will come back at some point. In the meantime graded readers are the best substitute for me.