That's 400 ppm of atmospheric CO2, of course as a symbolic (though hardly milestone) level is reached, and exceeded. The 400.03 ppm figure was reported by the US National Oceanic and Atmospheric Administration [NOAA] on May 10th. For the record, these are NOAA's figures over the last 1000 or so years.
Year CO2 ppm
~275 ppm was the level for most of human history it seems. Uncertainty figures are never quoted, but they must be small.
So what about temperature changes? And what about the link between CO2 and temperature change? For example, how much does temperature change if CO2 levels are doubled (the climate sensitivity)? And is this consistently found? Good questions!
This is all much more difficult and controversial than talking about CO2 levels. Here are some data about the last 100 years:
Averaged over all land and ocean surfaces, temperatures have warmed ~0.74ºC over the last century. More than half of this warming, about 0.4°C, has occurred since 1979.
Average global temperature on Earth has increased by ~0.8°C since 1880. Two-thirds of the warming has occurred since 1975, at a rate of roughly 0.15-0.20°C per decade
Global warming is now 0.8°C in the past century. 0.6°C in the past three decades
Source: US National Academy of Sciences
These are pretty consistent, but you need to know the uncertainty to make sense of the numbers. This is quite hard to find data on, but it turns out to be around ± 25% which is unsurprising given how difficult it is to measure Earth temperatures consistently over time.
I found the UK media coverage of the 400 break through rather muted, apart from the Guardian, which had a full and informed account, which is more than you could say about the 'discussion' at the end of the piece which almost reached down to the standards I normally associate with the Wiltshire Times. The Economist ended a recent article on climate change which discussed the models underpinning (and perhaps informing) our understanding of it, like this:
As a rule of thumb, global temperatures rise by about 1.5°C for each trillion tonnes of carbon put into the atmosphere. The world has pumped out half a trillion tonnes of carbon since 1750, and temperatures have risen by 0.8°C. At current rates, the next half-trillion tonnes will be emitted by 2045; the one after that before 2080.
Since CO₂ accumulates in the atmosphere, this could increase temperatures compared with pre-industrial levels by around 2°C even with a lower sensitivity and perhaps nearer to 4°C at the top end of the estimates. Despite all the work on sensitivity, no one really knows how the climate would react if temperatures rose by as much as 4°C. Hardly reassuring.