In addition to there being types of ice, there are types of ice age. Again this seems odd, but again the differences become important if we try to understand the climate. Depending on which of the three types of ice age we're concerned with, the answer to the question 'Are we in an ice age now?' is either no, we've been in one for 2.5 million years, or we've been in one for about 35 million years.
The first type of ice age is probably the most familiar. It really is asking 'Is there a whole lot of ice in the northern hemisphere?'. A little more specifically, it is about how much ice mass there is. While the area of snow cover and sea ice cover can be large, we don't think of that as being an ice age for this type. The ice age for this is when most of Canada and the northern USA are under 1-2 miles (1-4 km) of ice. The last time we were in that sort of ice age was about 15,000 years ago, give or take. Certainly we were done with it by about 7,000 years ago. Call this ice age type 'ice burying Chicago'.
The next sort is the 'ice burying Greenland' ice age. We've been in that condition continually since about 2.5 million years ago. Greenland is larger than Texas or France, so counts for having some significant size. The question here is 'Is there substantial ice anywhere in the northern hemisphere?' Before about 2.5 million years ago, back to over about 250 million years ago, the answer was no.
Those two types of ice age are biased towards an interest in the northern hemisphere. Since I, and most of the world's people, live in the northern hemisphere, I'm not entirely opposed to the bias. But, since I also am concerned about ice and ice sheets in their own right, let's consider the more general question for ice age 'Is there substantial ice anywhere on the planet?'
The answer to this is yes, and has been so for about 35 million years. Antarctica, sitting down on and around the South Pole, has had substantial ice since about then.
Now it isn't the case that we always have lots of ice somewhere on the earth. Prior to that 35 million years ago, you'd have to go back more than another 200 million years to find an ice age by the third definition. Over the history of the earth, it appears that ice ages are an unusual condition for the earth. Most of the time (over 80% in fact), the earth doesn't have any significant ice. Obviously to see it this way, we have to be taking a very long view of the earth's history.
For thinking about current climate, then, we want to be careful about what sort of ice age we're talking about. Some people refer to us 'still coming out of the ice age'. They're wrong for all three sorts of ice age. We were done coming out of the last 'bury Chicago' sort of ice age 7,000 years ago. And we're still in the other two sorts. If they were to end, sea level would rise by about 7 meters (about 20 feet) for the 'ice in the northern hemisphere' ice age, or about 70 meters (over 200 feet) for 'ice in the world' ice age. Since some hundreds of millions of people live less than 20 feet above sea level, I'd rather not come out of even just the northern hemisphere sort of ice age any time soon.