Quantum anomalies can be naively understood as the breaking of classical symmetries in the Lagranngian of a system due to quantum fluctuations. One of the simplest examples is the non-conservation of chiral charge (difference between number of right and left moving fermions) in a fermionic parabolic band under an electric field. It was realised more three decades ago that relativisitic fermionic field theories in 3+1 dimensions under magnetic fields host chiral Landau levels making them the idea platforms for studying such anomalies. More recently, the discovery of Weyl semimetals whose low-energy excitations are relativisitc Weyl fermions, and the synthesis of such systems in cold-atomic systems with artificial gauge fields has renewed the interest in the physics of quantum anomalies in the context of condensed matter and atomic physics due to the possibility of experimental verifications of such predictions. My interest lies in understanding how the quantum anomalies on lattice Weyl semimetals tie up the quantum field theoretic results and what is the fate of the anomalies on lattices in regimes not accessible in field theories.