We review experimental progress toward the understanding of a thermodynamic formulation of jammingingranular matter. Asaprelude of the dynamical measurements, westudyanovel compaction procedure at varying confining oscillatory pressures which ensures that the granular system has reached a reversible jammed state, i.e., the state of the system does not depend on the path taken despite the path dependency in the particle interactions. We then investigate the existence of an effective temperature with a thermodynamic meaning for jammed granular matter. The measurement of the effective temperature is realized in the laboratory by slowly shearing a closely-packed ensemble of spherical beads confined by an external pressure in a Couette geometry. All the probe particles, independent of their characteristic features and the shear rate, equilibrate at the same temperature, given by the packing density of the system. This suggests that the effective temperature is a physical variable for the nearly jammed system.