Quantum spin liquid state can be faithfully represented and efficiently characterized within the symmetric Projected Entangled Pair State (PEPS) framework. In this talk, I will discuss our works in recent years of constructing and characterizing both non-chiral and chiral SU(N) spin liquids with symmetric PEPS on the square lattice. Then I will present some recent results about SU(3) chiral spin liquid on the Kagome lattice using the same approach. If time permits, some further direction will be briefly mentioned.