Spin is fundamental in physics. Gravitation is universal. Searches for the role of spin in gravitation dated before the firm establishment of the electron spin in 1925. Since mass and spin or helicity in the case of zero mass are the only invariants of the Poincaré group and mass participates in universal gravitation, these searches are natural steps to pursue. Here we review both the theoretical and experimental efforts in searching for the role of spin/polarization in gravitation. We discuss torsion, Poincaré gauge theories, teleparallel theories, metric-affine connection theories and pseudoscalar (axion) theories. We discuss laboratory searches for electron and nucleus spin-couplings ---the weak equivalence principle experiments for polarized-bodies, the finite-range spin-coupling experiments, the spin-spin coupling experiments and the cosmic-spin coupling experiments. The role played by angular momentum and rotation is explicitly discussed. We discuss astrophysical and cosmological searches for photon polarization coupling. Investigation in the implications and interrelations of equivalence principles led to a possible pseudoscalar or vector interaction, and led to the proposal of WEP II (Weak Equivalence Principle II) which include rotation in the universal free-fall motion. Evidences for WEP II are discussed and compiled.Cosmological searches for photon-polarization coupling test the possibility of violation of EEP and the existence of cosmic pseudoscalor/vector interaction and may reveal a potential influence to our presently-observed universe from a larger arena. In relativistic gravity, there is a Lense-Thirring frame-dragging on rotating body with angular momentum. In analog with gyromagnetic ratio in electromagnetism, one can define gyrogravitational ratio. A profound search for the role of spin in gravitation is to measure the gyrogravitational ratio of particles. This could lead us to probe and understand the microscopic origins of gravity. We discuss the strategies to perform such experiments. R. Acad. Sci., Paris 174 593 Cartan É 1923 Sur les variétés à connexion affine et la théorie de la relativitée généralisée I, Ann. Ec. Norm. Sup. 40, 325 Cartan É 1924 Sur les variétés à connexion affine et la théorie de la relativitée généralisée I (suite), Ann. Ec. Norm. Sup. 41 1 Cartan É 1925 Sur les variétés à connexion affine et la théorie de la relativitée généralisée II, Ann. Ec. Norm. Sup. 42 17 Carroll S M, Field G B and Jackiw R 1990 Limits on a Lorentz-and parity-violating modification of electrodynamics Phys. Rev. D 41 1231-1240 Carroll S M and Field G B 1991 Einstein equivalence principle and the polarization of radio galaxies A experiment to search for vacuum dichroism, pseudoscalar-photon interaction and millicharged fermions Mod. Phys. Lett. A 22 2815 [arXiv:hep-ex/0611050v1] Cheng H-C, Luty M A, Mukohyama and Thaler J 2006 Spontaneous Lorentz breaking at high energies J High Energy Phys. 0605 076 Cheng K-S and Ni W-T 1980 Conditions for the local existence of metric in a generic affine manifo...