Both are based around a combination of three linear feedback shift registers with irregular clocking and a non-linear combiner. A5/1 is supposed to be the "strong" version for trustworthy countries, A5/2 the weak version for "others".
In 1999, Ian Goldberg and David Wagner cryptanalyzed A5/2 in the same month it was published, and showed that it was extremely weak - so much so that low end equipment can probably cryptanalyze it in real time. In 2000, Alex Biryukov, Adi Shamir and David Wagner showed that A5/1, although stronger, is still quite weak; after a moderately difficult preparation phase, it can then be cryptanalyzed in nearly real time.