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Neutrinos continue to provide a testing ground for the structure of thestandard model of particle physics as well as hints towards the physics beyondthe standard model. Neutrinos of energies spanning over several orders ofmagnitude, originating in many terrestrial and astrophysical processes, havebeen detected via various decay and interaction mechanisms. At MeV scales,there has been one elusive process, until a few years ago, known as coherentelastic neutrino-nucleus scattering (CEvNS) that was theoretically predictedover five decades ago but was never observed experimentally. The recentexperimental observation of the CEvNS process by the COHERENT collaboration ata stopped pion neutrino source has inspired physicists across many subfields.This has vital implications for nuclear physics, high-energy physics,astrophysics, and beyond. CEvNS, being a low-energy process, provides a naturalwindow to study light, weakly-coupled, new physics in the neutrino sector.  In this review, we intend to provide the current status of low energyneutrino scattering physics and its implications for the standard and beyondthe standard model physics. We discuss the general formalism of calculating thetree-level CEvNS cross section and present estimated theoretical uncertaintieson the CEvNS cross section stemming from different sources. We also discuss theinelastic scattering of tens of MeV neutrinos that have implications forsupernova detection in future neutrino experiments. We discuss how the CEvNSexperiments can be used as a testing ground for the Standard Model (SM) weakphysics as well as in searching for the Beyond the Standard Model (BSM) physicssignals. Any deviation from the SM predicted event rate either with a change inthe total event rate or with a change in the shape of the recoil spectrum,could indicate new contributions to the interaction cross-section.

Recent Progress in Low Energy Neutrino Scattering Physics and Its Implications for the Standard and Beyond the Standard Model Physics