Of course, to a scientist, unmet expectations are an opportunity, so a variety of papers have looked into why this has happened. They've found that, while volcanic eruptions seem to have contributed to the relatively slow rise in temperatures, a major player has been the El Niño/Southern Oscillation (ENSO), which has been stuck in a cool, La Niña state for most of the last decade. And, since climate models aren't expected to accurately forecast each El Niño, there would be no reason to expect that they would match the actual atmospheric record.
At least not intentionally. But some researchers have found that, simply by chance, a few of the models do produce an accurate ENSO pattern. And when those models are examined in detail, it turns out they match the existing temperature record pretty well.
The issue the new paper examines comes down to the difference between long-term climate trends and intermediate-term variations. In the long-term, the state of the climate is set by things like solar activity, orbital mechanics, and greenhouse gas levels, among other things. But on shorter time scales, things like volcanic activity and ocean cycles can have a profound effect on temperatures.
Coupled climate models that include both the atmosphere and the oceans accurately reproduce the behavior of the major ocean cycles, including the ENSO. But, since the onset of changes in the ocean is chaotic, the models generally don't get the timing right—the model may show an El Niño starting three years earlier than it does in reality.
If you're interested in how the models behave over a specific part of the historic record, that mismatch can be a problem, but there are several approaches to dealing with it. You can, for example, subtract out the influence of things like volcanoes and ocean circulation to see what the climate is doing without them. Or, rather than letting your model generate its own ENSO, you can force it to replay historic events in order to see what those do to the temperatures.
The new paper adds an additional approach to handling the problem: simply run a bunch of models and pick those that, by accident, accurately reproduced the ocean's chaotic behavior. The authors started with the CMIP5 collection of climate models and selected the 18 models that include an ocean simulation that's sophisticated enough to provide data on the state of ENSO and other ocean behavior. They started these 18 models in 1880 and used historical forcings (solar activity, greenhouse gas concentrations, etc.) up until 2005, then switched to a standard emission scenario until stopping the models in 2012.
If you look at the four models that were the worst at reproducing ENSO behavior, then you'd think climate modelers were incompetent, as these models all showed rapid warming from 1990 onward. But, if you picked the four that had the best match to real-world ENSO data, then you see exactly what reality produced: a relatively slow rate of warming starting at about the beginning of the century.