To reach the glacier and explore the ice cave, one starts at a far up the mountain valley. One must take a gondola ride down to half way point, followed by a long zig zagging staircase all the way down the rest of the glacier valley. Once there, one can enter the ice cave.
Every year, new ice caves must be dug, because the glacier (and therefore the caves) are continuously moving downhill. But not only must new caves be dug, new stairs must be added to the bottom...because the glacier is shrinking away.
Here is a picture of the glacier the way it looks today, 2012, at "ground level":
Had we visited in 2005, just seven years earlier, we would have climbed down and back up about 100 fewer stairs, because here is the level of the glacier caves then...the two pictures are of a sign marking the level, and a picture of the glacier taken from the sign.
Here is a perspective from 1990. The sign, and the ice blankets in the background mark the distance to the caves.
Here is another perspective from the level of the ice in 1990. Note the descending stairway all the way to the bottom left edge of the photo until it disappears out of sight.
Finally, 1980. Here is the level of the sign, then I turned around and snapped one from that same position in the direction of the ice. Note the winding stairway and the barely visible cave entrance.
Perhaps if one wants to visit the ice caves of Mer de Glace, they should plan on doing so soon?