Andrew Briggs developed the application of acoustic microscopy to image and measure the elastic structure of a wide range of materials, developing the theory to explain how cracks and other defects give rise to surface wave contrast. His 1992 monograph Acoustic Microscopy remains in print, with a new chapter on acoustically excited probe microscopy in the second edition (2010). With J.-P. Salvetat he used atomic force microscopy to determine the elastic constants of single-walled carbon nanotube ropes, subsequently extending the work to multiwalled nanotubes and biological microtubules.

He used high temperature scanning tunneling microscopy to obtain new insights into the surfaces of oxides that are insulating at room temperature and into the growth of semiconductors in real time. His atomic resolution images of surfaces of UO₂, NiO and CoO, and also TiO₂ and CeO₂ yielded information about the local electronic properties and bonding, paving the way for new theory. He used elevated temperature STM to understand homo- and heteroepitaxial growth on silicon surfaces. By using gas precursors he was able to visualize growth directly in real space with atomic resolution in real time, from single atom dynamics to growth of several monolayers.

He initiated new studies of carbon nanotubes as containers for chemical reactions and has been at the forefront of developing molecules for quantum technologies. His work on electronic properties of nanostructures led him to devise methods for entangling states in quantum dots, and a scheme for solid state quantum computing based on a combination of single-walled carbon nanotubes and endohedral fullerene molecules. To characterize the required nanostructures, he used of low voltage TEM to image sp²-carbon materials: fullerenes, nanotubes, and graphene.

He showed how sophisticated pulse control techniques could be harnessed for high fidelity operations on electron spins, using bang-bang control to manipulate a nuclear spin rapidly via an electron spin, which in turn led to techniques for transferring information between electron and nuclear spins of molecules and of impurity atoms in silicon. He invented a method for storing information from superconducting qubits in collective spin states and performed semi-classical proof-of-principle experiments.

He directed the Quantum Information Processing Interdisciplinary Collaboration, which was followed by UK investment of £270M in Quantum Technologies. He leads major programmes to investigate quantum effects in electronic nanodevices for low energy information and communication technologies, and use hardware-in-the-loop simulations for testing quantum sub-components to accelerate their route to innovation. His patented method of forming nanogaps in graphene is being developed for genome sequencing.

He realised that extending the limits of non-classical behaviour in nanomaterials systems both raises afresh foundational questions about the nature of reality, and provides new means to address them. He devised a new experiment which tested the Leggett-Garg inequality using truly non-invasive measurements. His new book with Roger Wagner, The Penultimate Curiosity, was published by Oxford University Press in February 2016, with endorsements on the cover from a former President of the Royal Society, the Director General of CERN, a former Chief Rabbi, and the Archbishop of Canterbury.