Hello there, an economics undergraduate here!
Luckily for us, our professor, Brian Snowdon, authored papers and even two books on the topic of the great divergence and global growth.
The Great Divergence is defined by Samuel Huntington as the still-growing divide between what's perceived as the "West" and the developing world.
To understand the Great Divergence, look at the "Tiny Divergence" first which occured in the 19th century and can be argued as a reason for WWI.
The industrial revolution started in Britain, and radiated from the British Isles in waves. More on the "why there" later. However, the industrial revolution brought a couple new things:
Production overcame consumption, subsistence economies were transformed into capital-stockpiling economies of sustained growth
Economies of scale were developed and nations began to accumulate wealth as per the Solow Growth model
Understand the event of industrialisation in a certain country as "making a deposit" into a bank, and then starting to accumulate compound interest. What growth you had in year one contributes to the growth in year two, both contribute to year three and so on. Exponential growth, in short.
This mechanic provided a terrifying advantage to nations where the industrial revolution began earlier. The main nations, in vague order of industrialisation, are: UK (British Empire), USA, Germany (North German Confederation / Prussia), France, Austria (Habsburg Empire), Russia.
You can see that this list basically equals to the power weights in World War One. Exactly, the issue of WW1 was that the newly united Germany's industrial growth far superseded Britain's, and thus the compound growth of Germany was catching up to the British one. The Little Divergence retained its early form /because/ nations went to war to retain it.
Compare the sheer differences apparent even today between the first industrialised European superpower (UK) and the last one (Russia). Sure thing, both had empires collapsing, crises, stagnations but they /are/ part of the Great Divergence.
Now imagine how industrialisation started a whole century later in the developing world (or in the case of Sub-Saharan Africa, it still hasn't started!). This difference is very hard to combat, some Asian countries succeeded with foreign aid and an immense investment in education.
So, the great divergence was triggered by the delay in the spread of the industrial revolution.
The delay in the spread of the industrial revolution was caused by a limit on how knowledge and capital could spread, and by the factors that allowed Britain to spark it in the first place. These factors are, as listed by the professor previously mentioned:
The Enlightenment in Europe and the promotion of innovation and invention (more on that in The Gifts of Athena, Joel Mokyr). The protection of intellectual rights, and the establishment of scientific journals in Europe (their amount quadrupled between 1750 and 1800). Compare this to the limits imposed by religion anywhere else than Protestant countries.
A restraint on "rent seekers", a limit on criminal activity, security of private property and capital. The weakness of the British Crown and the only "functioning" parliamentary democracy. Compare this to the Chinese administration's influence.
Now is this a scholarly concensus? More or less, yes. Some quote colonial exploitation, but colonial exploitation was made available (and a necessity) by enormous growth, resulting from the industrial revolution. I do not know about any other scholarly theory around the Great Divergence. The debate revolves mostly around whether the Divergence continues, or whether there is a convergence.