Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f$_+$(0), arising in the semileptonic K $\to \pi$ transition at zero momentum transfer, as well as the decay constant ratio $f_{K}/f_{\pi}$i and its consequences for the CKM matrix elements V$_{us}$ and V$_{us}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)$_L$ x SU(2)$_R$ and SU(3)$_L$ x SU(3)$_R$ Chiral Perturbation Theory. We review the determination of the B$_K$ parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ (also new compared to the previous review), as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant $\alpha_s$