I have posted on problems before: HERE and HERE. As mentioned, I've never been a big fan of them in the past, but recently after reading some articles on problem solving and actually trying (mostly unsuccessfully) to do a few, I have discovered that I've been missing out on another enjoyable aspect of the game. So far I am not very good at solving...I am still learning terminology and themes, but eventually, I hope to be more successful as I learn what to look for.
Just as in OTB play, the titles International Grandmaster, International Master and FIDE Master are awarded by FIDE via the PCCC (Permanent Commission for Chess Composition) for especially distinguished problem and study composers and solvers.
For composition, the title of Grandmaster for chess composition was established in 1959, with André Cheron, Arnoldo Ellerman, Alexander Gerbstmann, Jan Hartong, and Cyril Kipping being the first honorary recipients. In subsequent years, qualification for the IM title, as well as for the GM title (first awarded in 1972 to Genrikh Kasparyan, Lev Loshinsky, Comins Mansfield, and Eeltje Visserman) and the FM title (first awarded 1990) has been determined on the basis of the number of problems or studies a composer had selected for publication in the FIDE Albums. These albums are collections of the best problems and studies composed in a particular three-year period, as selected by FIDE-appointed judges.
There are also titles for solvers. For solvers, the GM (International Solving Grandmaster) and IM titles were both first awarded in 1982; the FM title followed in 1997. GM and IM titles can only be gained by participating in the official World Chess Solving Championship (WCSC). The title International Judge of Chess Compositions is given to individuals considered capable of judging composing tournaments at the highest level.
Wikipedia article, Here is an informative pdf book, 101 pages: Chess Problems Made Easy, Start Solving Now Part 1 (USCF article), Start Solving Part 2 (USCF article), Compose like Mozart (USCF article), British Chess Problem Society - This is a great site.