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Usually, when physicists search for a new theory it’s because they have encountered something in the world that cannot be explained by the current theories. Such was the case, for example, with the development of quantum mechanics, which began with the anomalous experimental phenomena of the spectrum of blackbody radiation and the photoelectric effect; and also for the development of special relativity, prompted by asymmetries in the predictions of Maxwell’s electrodynamics which – famously – did not seem to accord with nature. In these instances, observations precede, and go hand-in-hand along with, the theoretical work: motivating, guiding, and constraining it. Yet, this is not so for the current search for a new fundamental theory of physics, known as quantum gravity, which – although potentially related to some empirical problems – has been primarily motivated, guided, and constrained by theoretical and philosophical considerations (but cf. §1.3). The search for a theory of QG has grown into one of the greatest challenges in modern physics. It is my contention that one of the reasons for the difficulty in finding a theory of QG is that it is not clear what the theory is supposed to achieve, and what, in fact, it should be expected to achieve. Thus, a better understanding of the motivations for seeking the new theory can help us to more precisely frame, and eventually answer, the question ‘What is the problem of QG?’ The hope is that critical investigation of the theoretical and conceptual problems which motivate the theory can reveal some of the principles (or prejudices) which may underlie these problems. We can then assess whether these principles are well founded, as well as the consequences of adopting them in various roles in theory-development, especially in conjunction with other principles and constraints. It is an aim of this Element to introduce and instigate this new, critical perspective upon the problem of QG. As such, this Element will not cover all of the important developments and philosophically interesting aspects of QG; in particular, discussion of spacetime emergence, spacetime functionalism, and the AdS/CFT duality are conspicuously absent. So, why do we want a theory of QG? The usual answer refers to ‘two pillars’ of fundamental physics: general relativity (GR), providing our best understanding of spacetime, and quantum mechanics (QM), our best understanding of matter.1 Both these frameworks are supposed to be universal: unrestricted in their domains of applicability, that is, both are supposed to describe everything in the universe. In practice, however, we typically only need to use GR to describe ‘big stuff’ (the universe at large distance scales), and QM to describe ‘small stuff’ (matter and forces at short distance scales, or, equivalently, highenergy scales). Yet, there are domains of the universe (‘parts of the world’) where both GR and QM are thought to be necessary – where we cannot get away with just using one or the other theory, or any known combination of both. These domains are characterized by extreme densities or temperatures (potentially as high as 1093 grams per cubic centimetre, or 1032 degrees Celsius), and include the cores of black holes (within the Planck length 10−35 m), cosmological singularities such as the ‘big bang’, and the first instants of early universe cosmology. The desire for a description of these domains is part of the primary motivation for seeking the new theory of QG.