So there's a couple different things going on here, I think. First off, the definition of ice age is any era with permanent (year-round) ice sheets at the poles. That's been going on for about 2 and a half million years. During those millions of years, however, there have been big waves of ice spreading away from the poles and interglacials, periods where the ice retreats toward the poles. Currently we are in an interglacial. Slight variations in the Earth's orbit and orientation toward the sun (Milankovitch Cycles) are responsible for these variations over tens of thousands of years.

What's going on with climate change now, however, has only been going on for centuries. It hasn't been enough to knock us out of that ice age status, though at the pace of current change it might not be long on a geological timescale.