I’m assuming this refers to the next period of glaciation, or what’s popularly called an “ice age” as technically speaking we are already in an interglacial within an ice age - it counts as an ice age because we have ice at the poles, and for long periods of geological history the poles were ice free. That’ happens because the North pole’s Arctic ocean is enclosed by land masses and we have land at the South pole, both unusual situations that happen rather rarely in the geological record as the continents drift:

So, in that sense, of what is popularly called an “ice age”, then up to a seminal paper in 1976, it was thought that we were headed for a new ice age quite soon. But in that paper a nineteenth century theory called the Milankovitch cycles was confirmed, according to which ice ages arise due to the interactions of several slowly changing properties of the Earth.

This is the best summary I've seen of it anywhere:

• "A) against the backdrop of the stars, the whole axis of the earth gyrates like an out-of-balance spinning top in a 25,770 year cycle
• "B) the ellipse of the earth’s orbit around the sun is itself turning against the background of the stars in a 21,000 year cycle.
• "C) the obliquity of the Earth ranges between 22.1° & 24.5° in a 41,000 year cycle, mainly under the influence of Jupiter
• "D) the eccentricity of the Earth’s orbit changes in a complicated manner in cycles of 96,000 and 413,000 years"

For details see Variation in the Equation of Time.

The new research starting in 2002 showed that we are not headed for an ice age for about 100,000 years, whatever happens.

That’s because of the variation in eccentricity of the Earth's orbit cycle. We are headed towards a time when the Earth's orbit is almost circular, and when that happens, then the other Milankovitch cycles have almost no effect.

The last time this happened was 400,000 years ago. The Antropogenic CO2 will make a difference there, make the Earth a bit warmer than it otherwise would be, and the CO2 we have already added, if not removed in some way, will affect our climate subtly for tens of thousands of years into the future, and may cause the Antarctic ice sheet to melt eventually. But we weren't headed for a new ice age for 100,000 years anyway according to this study which I think is now generally accepted.

They found that our current CO2 levels would have to be as low as 220 ppm to enter a new glaciation before 100,000 years from now. That is lower than the 280 ppm of CO2 we had for the 10,000 years leading up to 1750.

A couple of extracts from the paper:

"The small amplitude of future insolation variations is exceptional. One of the few past analogs (13) occurred at about 400,000 years before the present, overlapping part of MIS- 11. Then and now, very low eccentricity values coincided with the minima of the 400,000-year eccentricity cycle. Eccentricity will reach almost zero within the next 25,000 years, damping the variations of precession considerably."

...

"Most CO2 scenarios led to an exceptionally long interglacial from 5000 years before the present to 50,000 years from now (see the bottom panel of the figure), with the next glacial maximum. Only for CO2 concentrations less than 220 ppmv was an early entrance into glaciation simulated.!"
On the Precession as a Cause of Pleistocene Variations of the Atlantic Ocean Water Temperatures

That of course is well below any CO2 levels including pre-industrial levels. CO2 was at 280 ppm for 10,000 years up to the mid C17, it was 399 ppm for the global averaged yearly average temperatures for 2015 (Annual temperature means). It's set to reach over 400 ppm for the average for this year, as you can see from the monthly figures:.

ESRL Global Monitoring Division

We are also possibly headed for a “mini ice age” for the next 30 years. The name is dramatic but it doesn’t actually mean a glaciation period. Last time it happened then it got cold enough for people to skate on the river Thames in London. But it’s a warmer world now, and it’s just a fraction of a degree temporary reduction in temperature if it happens at all, as it is just an unproven theory at present.

If it is correct, not verified yet, this may offset some of the effects of climate change for a few decades, not reverse the effects, just appear to slow it down - though of course it has no effect on ocean acidification. However, except for the effects on the oceans, this may give us a bit of a breather. It would of course still be urgent to do something about it as, after leveling off for a few decades, the temperatures would then rapidly soar to the predicted values for 30 years from now. The global temperatures would not be expected to fall at all during this period even if the theory is correct.

This research was widely misreported, with newspaper headlines saying dramatic things such as that the sun’s output would decrease by 60% for 30 years. That indeed would have a very dramatic effect on climate if true. Actually the paper said the number of sunspots would decrease by 60%, a little bit of a difference there (British ironic understatement :) ).

See The 'mini ice age' hoopla is a giant failure of science communication

Also even the worst projections of climate change will not take us out of our current geological ice age, at least not for a long time. If eventually the Antarctic ice sheet did melt, that would count as coming out of the geological ice age, but that is not going to happen for thousands of years. The Earth has been far warmer than this in the past. What makes it difficult for us is not the absolute temperature, but the rate at which it is changing. Especially, plants can’t move quickly, as they need to seed a new generation to move, which for trees can take decades. And animals also can be sensitive to small changes in temperature and may have nowhere nearby to move to, for instance in tropical rainforests, a small increase in average temperature can lead to many extinctions because the creatures there are adapted to very stable conditions.

Also we have many people that live in low lying places, with Bangladesh most affected, which would be flooded by small increases in sea level. The sea level rises through thermal expansion of the oceans, and there is a delayed effect there - the warming we’ve already had will cause the sea to continue to rise for centuries into the future. https://www.ipcc.ch/ipccreports/... Other effects also increase the levels such as melting of land ice in Greenland and Antarctica (changes in the amount of sea ice in the Arctic have no effect since ice floating on the sea is in equilibrium with the ocean already) Sea Level Rise -- National Geographic.

And the increasing warmth of the Earth’s lower atmosphere leads to more energy in the system so increasing the potential for extreme weather events like tornadoes, hurricanes etc and increasing rainfall and flooding. 13. How does climate change affect the strength and frequency of floods, droughts, hurricanes, and tornadoes?

So - those effects are mainly important because they affect humans, because we have chosen to colonize low lying places, and because we create buildings, roads etc that are affected by extreme weather events, and our agriculture also. But the rising temperature affects other species, so does the acidification of the oceans. The land species could move if the temperature rises happened more slowly. The ocean acidification happens from time to time naturally, over geological timespans, in that case it does lead to extinction of corals. Which then get replaced, interestingly, by a completely different mix of species next time corals independently evolve in a lower pH ocean. So - there an ocean without coral is a natural thing that happens from time to time, but is unnatural for us if we end up with one, because we are in a geological era that has lower levels of CO2 and so normally has coral reefs.

I think it helps to have this perspective, that climate change is not taking Earth into any kind of unprecedented state, it’s been far warmer and had far more acid oceans too in the past. It’s the speed of the change (which affects many species), plus the fact that there are so many humans dependent on the climate conditions as they are now in various ways, that is the main matter of concern.

See also:

A Short Introduction to Climate Change

ESRL Global Monitoring Division