Numerical methods are a powerful tool for doing calculations in spinfoam
theory. We review the major frameworks available, their definition, and various
applications. We start from sl2cfoam-next, the state-of-the-art
library to efficiently compute EPRL spin foam amplitudes based on the booster
decomposition. We also review two alternative approaches based on the
integration representation of the spinfoam amplitude: Firstly, the numerical
computations of the complex critical points discover the curved geometries from
the spinfoam amplitude and provides important evidence of resolving the
flatness problem in the spinfoam theory. Lastly, we review the numerical
estimation of observable expectation values based on the Lefschetz thimble and
Markov-Chain Monte Carlo method, with the EPRL spinfoam propagator as an
example.Comment: 33 pages, 11 figures. Invited chapter for the book "Handbook of
Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer
Singapore, expected in 2023