Of course, there are caving magazines too. Here is just a small list of them:
)
                Le magazine de la spéléologie d’exploration, the "most beautiful caving magazine in the world".
            
)
                A UK based magazine, not longer available.
            
)
                Another UK based magazine with an enviable reputation.
            
)
                The magazine for subterranean images. Specialized on cave photography.
            
)
                Official publication of the Verband österreichischer Höhlenforscher (Austrian Caving Society).
            
) The German Caving Society publishes a magazine with 4 issues per year. Scientific articles with English abstracts (
). The link
                leads to the homepage, but there is no separate page for the magazine. Have a look at the 
List of Publications (pdf file) instead.
            
)
                German publication of some caving clubs in northern Germany.
            
)
                German publication by the Höhlen- und Heimatverein Laichingen, a south German caving club. Published twice a year. Contains typically several scientific articles per issue. English abstracts
                (
).
            
)
                Polish magazine, very good reputation. They also publish Polish Caving in english (
).
            
)
                One of several publications of the Società Speleologica Italiana (Italian Caving Society).
            
)
                A scientific publication of the American Spelean History Association (ASHA).
            
)
                Publication of the Verein für Höhlenkunde München (Munich Caving Club)
            
). The quarterly scientific publication of the National Speleological Society.
). The monthly publication of the National Speleological Society. Trip reports, events and colour images.
) official publication of the Hellenic Speleological Society, the Greek Caving Society.Additionally there are numerous other magazines which contain articles about caves now and then. Mostly these are geographic magazines.