Our understanding of the fundamental forces and particles in nature is based on a framework called quantum field theory (QFT). This framework however does not seem to be suitable to describe the gravitational force as a quantum field theory. Both technical and conceptual issues arise when one tries to use the QFT machinery to describe gravity. String theory is a framework in which quantum gravity can be described through. However since our understanding on string theory was limited to a perturbative description it was hard to study many questions. This changed with the discovery of the AdS/CFT correspondence. This amazing idea claims that a string theory in a background space time called Anti-de-Sitter space (called the bulk) is in fact alternatively described by a normal QFT (in this case a conformal field theory) that lives in one lower dimension (called the boundary). This correspondence is also called a holographic theory, since the space-time the string theory lives in (our world, roughly speaking) and all of the local physics in it , is emergent from a QFT description that lives in one lower dimension.
How exactly is the physics of the bulk encoded in the boundary theory. One long time theme is the construction of local bulk operators from the fundamental degrees of freedom of the boundary theory. This in fact is tightly connected to an old problem in quantum gravity, which is how does one construct semi-local physical observables in a theory of gravity. This is also connected to the so called problem of time in quantum gravity. Apparently using ideas from AdS/CFT one can answer some of these long standing questions, and the inquiry into these through this lens have uncovered interesting connections between different objects appearing in conformal field theories, and also interesting connections with quantum information.
Conformal field theories (CFTs) describe physical systems at their critical point, undergoing second order phase transitions. A remarkable aspect of CFTs is that there are methods to solve them even at strong coupling, due to their high degree of symmetry. This is the goal of the conformal bootstrap program, which makes use of numerical and analytical tools to solve the crossing equations of a CFT.
One of the important new tools of the conformal bootstrap are dispersion relations. Dispersion relations enable to construct correlation functions from their singularities. Dispersion relations can be used to relate the high energy (UV) physics with the low energy (IR) physics of a theory. Moreover, dispersive techniques enable to constrain effective field theories of gravity, and as a result they have recently played a role in the swampland program.
Another interesting aspect of the holographic ideas is the ability to compute certain properties of strongly coupled quantum field theories through the study of the classical properties of the dual string theory. Certain interesting condensed matter phenomena such as super-conductivity, super-fluidity , fractional quantum Hall states, strongly coupled anyons, etc , can be studied with new tools.