Quantum spin liquids represent one of the most fascinating yet elusive phases of matter, characterized by long-range entanglement and fractionalized excitations. In this seminar, I present a unified tensor network framework for understanding Kitaev spin liquids and their neighboring phases. Starting from a compact loop gas (LG) and string gas (SG) construction for the spin-1/2 Kitaev honeycomb model [PRL 123, 087203 (2019)], I show how the key features of the gapless Kitaev spin liquid — including symmetries, Z₂ gauge structure, criticality, and vortex-freeness — emerge naturally in the tensor network language without invoking Majorana fermions. This framework is then extended to the star lattice, where both Abelian and non-Abelian chiral spin liquids are identified through minimally entangled states and their entanglement spectra [PRB 101, 035140 (2020)]. I further discuss applications to realistic Kitaev magnets under magnetic fields using infinite tensor product states, revealing novel nematic paramagnetic phases in the K-Γ-Γ′ model [Nat. Commun. 11, 1639 (2020)], and to the spin-1 Kitaev model, where a gapped Z₂ spin liquid with Abelian anyons is established [Phys. Rev. Research 2, 033318 (2020)]. Finally, I present a recent development showing that the interplay between global and local symmetries of the quantum transfer matrix provides a powerful diagnostic for topological phases, enabling the identification of symmetry-enriched criticality and symmetry-protected edge modes without extensive numerical simulations [Sci. Rep. 16, 1586 (2026)].