This week, thousands of diplomats from across the globe are gathered in Lima, Peru, to start hashing out a new agreement to address global warming. The hope is that they'll have a final deal in place by the end of 2015.

It's a daunting task. Scientists warn that the world is currently on pace to heat up around 4°C (7.2°F) or more by the end of the century. That much extra heat could have disastrous consequences: the eventual loss of Greenland's ice sheet, steep sea-level rise, crop failures, mass extinctions, and so on.

Even if we zeroed out fossil-fuel emissions, the world would still be hotter in 2100

The clearest way to avoid that fate is to reduce global greenhouse-gas emissions in the coming decades. But even if the world managed to zero out fossil-fuel emissions this century — an exceedingly ambitious goal — we may still be on pace for 2°C (3.6°F) or more of warming by 2100. That's not quite as drastic, but it would still mean some amount of sea-level rise, widespread flooding, increased drought, and so on. Poorer countries, in particular, could struggle to adapt.

So the point of the UN talks is for countries to figure out how best to navigate this increasingly difficult situation: How much should global emissions be cut? What actions should individual countries take? How much aid should wealthier nations offer to poorer nations to adapt to whatever level of warming we do get? These questions won't all get answered definitively by 2015, but the hope is for an agreement that at least gets things started.

In the past, these talks have often been gridlocked by deep disagreements over how to divvy up these tasks. Poorer countries have argued that the US, Europe, and other rich nations are to blame for most of the man-made carbon-dioxide currently in the atmosphere, so they should bear the burden for both cutting emissions and providing aid to poorer countries. Richer countries, for their part, argue that you also have to look at future emissions to tackle the problem — so fast-growing nations like China and India need to do more.

In November, the US and China had a mini-breakthrough of sorts on this impasse when both countries pledged to curb their emissions between now and 2030. That's led to some optimism about these upcoming talks. But that deal wasn't enough, on its own, to decisively alter the trajectory of global emissions and avoid 4°C or more of warming. A lot more is still needed for that.

So below are 7 key charts from the Global Carbon Project that give a sense for what's at stake in these talks — and why it's so difficult to come to a deal:

1) T he world is currently failing to meet its climate goals

Let's start with the big picture on climate change. The black line above shows the current growth of annual carbon-dioxide emissions worldwide. The colored lines show various future pathways and what they'd mean for global warming.

We're currently on pace for somewhere between 5.8°F and 9.7°F of warming

The world's nations have all agreed that it would be "dangerous" to allow global average temperatures to rise more than 2°C (or 3.6°F) above pre-industrial levels. (See here for why.) But to have a decent chance of staying below 2°C, global emissions would likely have to follow the blue or yellow trajectories — peaking in the very near future and declining sharply by century's end.

Instead, emissions keep rising. And if emissions continue on their present course, scientists estimate, we can expect somewhere between 3.2°C and 5.4°C of warming by the end of the century (that's between 5.8°F and 9.7°F). Various reports have warned that this would entail dramatic and irreversible changes, like destabilizing Greenland's ice sheet or large-scale extinctions. The World Bank, for one, thinks this much warming could be impossible for many countries to adapt to.

Recently, countries like the United States, Europe, and China have all made various pledges to reduce their emissions in the future. But even if you take all those pledges seriously, analysts at the Climate Action Tracker have found that we're still on pace for between 3°C and 4.6°C of warming by century's end. That's not much better. (The range is largely due to uncertainty over exactly how the climate would respond to so much carbon — but scientists are quite confident that it would get a lot hotter.)

2) We'll blow through our "carbon budget" for 2°C in 20 to 30 years

Here's another way to look at the climate issue. If we want to avoid more than 2°C of global warming, scientists estimate, then humans can only put about 3,200 gigatons of carbon dioxide into the atmosphere. (This gives us a two-thirds chance of staying below the limit.)

We're about two-thirds of the way through our carbon budget

Since the Industrial Revolution, we've loaded roughly 2,000 gigatons of carbon dioxide into the atmosphere. So we only have about 1,200 gigatons left. And at current growth rates, we'll blow through that in about two or three decades.

That's our "carbon budget." Meeting the 2°C goal would, in theory, entail divvying up the remaining 1,200 gigatons among various countries. Country A gets to emit this much carbon. Country B gets to emit this much carbon. And so on. But that's incredibly hard to do. For one, setting these sorts of top-down goals hasn't had much success to date. And, as we'll see below, allocating responsibility isn't easy.

By the way, there's a good argument that the 2°C limit has become impossible, and that something like 3°C (or 5.4°F) is a more realistic goal. If that were the case, the carbon budget would be a bit bigger (we'd have around 2,000 to 2,500 gigatons left), but we'd still be on pace to blow through it within several decades.

3) The US and Europe are responsible for much of the CO2 already in the atmosphere...

Now comes the blame game. The chart above shows cumulative emissions from fossil fuels and cement over time. For any given year, it more or less shows who is responsible for what fraction of the carbon-dioxide in the atmosphere.

The US and Europe have had their fossil fuel party, now India and China want theirs

As you can see, the United States and Europe are responsible for 49 percent of all carbon emissions from fossil fuels and cement that have been emitted since 1870. They've long enjoyed the growth benefits from using fossil fuels — and now other countries want theirs. This chart also explains why many people put the blame for current global warming squarely on the United States and Europe and are asking for aid to adapt.

But the US and Europe, by contrast, argue that the situation is now shifting rapidly. If you only look since 1990, China has been responsible for 20 percent of the cumulative emissions in the atmosphere — more than Europe (14 percent) and on par with the United States (20 percent). That's why wealthier nations often point instead to charts like the one below:

4) ...But nowadays it's developing countries who emit the most carbon

The previous climate treaty — the Kyoto Protocol of 1997 — divided the world into two sections: wealthy nations ("Annex B") and developing countries ("non-Annex B"). The former were supposed to cut their emissions. The latter were allowed a free pass so that they could keep growing.

Emissions from wealthy nations are declining

As the chart above shows, that more or less happened. Annual emissions from Europe, the United States, and other wealthy "Annex B" countries are declining, albeit slowly. But emissions from developing countries have exploded.

Today, developing countries produce 58 percent of the world's annual carbon-dioxide emissions. China alone is responsible for 27 percent. This is why negotiators from wealthy countries often insist that China and other poorer countries need to commit to reductions in any new treaty. China, for its part, has recently pledged to have its emissions peak by around 2030 (although it won't say at what level). It remains to be seen if other developing countries follow suit.

5) China's per capita emissions are now higher than the EU's

Here's another chart on the same theme. China's overall emissions are currently higher than those of the US or Europe. But Chinese negotiators have long argued that that's only fair — after all, China has 1.3 billion people, so of course it's emissions will be higher.

But now China is crossing a different threshold. It's per capita emissions are actually higher than those in Europe. (They are still far below America's, although America's have been dropping sharply.)

By the way, that chart above also shows why India is so reluctant to heed calls to reduce its emissions — especially when its per-capita emissions are still so low and 300 million people still have no access to electricity.

6) That's partly because rich nations are "outsourcing" their carbon

Here's another tricky issue. Emissions can also be "outsourced" abroad. Say, for instance, a US factory moves to China and produces goods that are then shipped back to the United States. America's emissions decrease. China's emissions increase. But who's responsible for that carbon, really?

This isn't a trivial issue. The Global Carbon Budget 2014 report notes that virtually all of the reductions in emissions made by wealthy countries like the US and Europe since 1990 have been offset by "outsourced" emissions to places like China. These emissions transfers are now growing at a rate of 11 percent per year.

7) Divvying up the remaining carbon budget is... complicated

So now, if we want to stay below the 2°C limit (or 2.5°C or 3°C), negotiators have to take all of the factors above and come up with some way to divvy up the remaining carbon budget.

As this chart from the Global Carbon Project shows, there are lots of ways to do this. Negotiators could agree to let everyone maintain their current share of emissions (an "inertia"). The United States emits 18 percent of the world's emissions today and gets 18 percent of the remaining carbon budget. But that's not terribly fair, since India would get penalized for being poor — it would miss out on the growth benefits of burning fossil fuels.

Alternatively, you could take an "equity" approach. India is a big and poor country in dire need of more growth. So it should be allowed to take up a bigger share of the carbon budget. The United States and Europe get a much smaller share, by contrast — they need to enact draconian emissions cuts. The problem is that it's not clear whether this is even technically feasible.

A third approach, described here, is a "blended" approach that tries to compromise on all these different issues. A recent paper in Nature Climate Change argued that this was the best way to stay below the carbon budget. Whether national governments agree with that, of course, is another story.

More realistically, the world's nations will set their own individual goals based on what they each think makes the most sense for themselves. Most analysts think this is the most likely outcome of the current UN talks — each nation sets voluntary goals for themselves and the new treaty sets up some sort of monitoring and verification mechanism.

Now, whether all those voluntary pledges add up to staying within the carbon budget and below 2°C is much less clear. Which brings us all the way back to chart #1 up top…

Further reading

Past UN climate talks have failed. Will this one be any different?

How to stop global warming, in 7 steps.

An in-depth look at the 2°C climate goal — and what happens if it's no longer feasible

Here's what the world would look like if we took global warming seriously