Spelunx has no real story, and is meant as a game to be explored and played with rather than completed. Other than the player, there are two main characters, Professor Spelunx and Mr. Seudo, who are pictured but never actually meet the player. Robyn Miller hand-drew all of the graphics in the game.
In the 1993 colorized release, Cyan's Myst made a cameo appearance in the Tumnus room. You can view a picture of Myst Island by dragging the x-ray viewer on the model house to the bottom right hand corner of the screen.