Of course, there are caving magazines too.
Here is just a small list of them:
Spéléo () Le magazine de la spéléologie d'exploration, the "most beautiful caving magazine in the world". There is only a French version at the moment, but they're planning an english version in the future.
The International Caver
A UK based magazine, not longer available.
Descent () Another UK based magazine with an enviable reputation.
Der Antiberg, Mitteilungen zur Karst- und Höhlenkunde () German publication of some caving clubs in northern Germany.
Laichinger Höhlenfreund () 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 ().
Jaskinie (The Caves) () Polish magazine, very good reputation. They also publish Polish Caving in english ().
SPELEOLOGIA () One of several publications of the Società Speleologica Italiana (Italian Caving Society).