Results from LHAASO and HAWC have revealed a new picture about the gamma-ray sky reaching energies above hundreds of TeV. Additionally, because of their high duty cycle (>95%) and wide field of view, both observatories will complement results from telescope arrays, like MAGIC and the future CTAO, and extend observations from Fermi-LAT. Two important advantages are the opportunity to perform population studies and long-term monitoring of the gamma-ray sky. For example, population studies of galaxy clusters should help to put tight constraints on parameters related to dark matter (DM) candidates as WIMPs, axion-like particles (ALPs) or dark photons; but also to search for diffuse emission induced by cosmic-ray protons, and help to understand the dynamic and evolution of clusters. Long-term monitoring could also help to have a better idea of the constant/quiescent emission and search for variability in all the TeV gamma-ray sky at different timescales. In this talk, I will present some details about the status of the on-going analysis on these three topics using LHAASO and HAWC data.
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