The latest results for measurements of electroweak (EW) boson pair production of V$\gamma$ (V$=$W or Z) plus two jets ($\mathrm{j}$) in LHC proton-proton collisions at a center-of-mass energy of 13 TeV are presented. The measurements are performed in final states of $\ell\ell\gamma\mathrm{jj}$ and $\nu\nu\gamma\mathrm{jj}$ in Z boson decay modes and $\ell\nu\gamma\mathrm{jj}$ for W boson decay with the data recorded by the CMS and ATLAS detectors in 2016-2018 corresponding to integrated luminosities of 137 and 139 fb$^{-1}$. The inclusive or differential cross sections are measured with a large dijet mass required close to the phase space of the vector boson scattering (VBS) or fusion (VBF) process. Exclusion limits on anomalous quartic gauge couplings (aQGCs) based on the dimension eight operators of the effective field theory are derived at 95\% confidence level. The upper limits of searches for a 125 GeV Higgs boson to invisible particles (H$\rightarrow\chi\chi$) and a dark photon (H$\rightarrow\gamma\gamma_{d}$) are set in the Z$(\nu\nu)\gamma\mathrm{jj}$ measurement assuming the Standard Model (SM) production cross section.