Pore connectivity, a topological characteristic of pore structure, is oftentimes more important than the geometrical aspects in controlling fluid flow and mass transport in porous natural rocks as well as their associated utilities in energy and environmental stewardship. A different extent of pore connectivity can be reflected in the proportion of isolated pore space not connected to the surface of natural rocks. This work presents the multi-approach and multi-scale laboratory studies to investigating the proportion of isolated pore space of, and its resultant anomalous fluid flow and radionuclide movement in, generic geological barrier materials (clay sediment, crystalline rock, salt rock, shale, tuff). The samples include clay sediments of Wakkanai formation at Horonobe underground research center in Hokkaido of Japan, Opalinus clay of Mt. Terri Underground Research Laboratory as well as granodiorite from the Grimsel Test Site in Switzerland, salt rock from Waste Isolation Pilot Plant in New Mexico, various shales (Barnett, Eagle Ford and Wolfcamp from Texas), and welded tuff in Yucca Mountain in Nevada. Working with sample sizes from <75 μm to several centimeters, the experimental approaches include the independent quantification of both (1) surface-accessible pore space with various probing fluids (e.g., helium in expansion, water in vacuum saturation and nuclear magnetic resonance, mercury in intrusion porosimetry, nitrogen in gas physisorption, and Wood’s metal in high-pressure impregnation and micron-scale tracer mapping using laser ablation-ICP-MS); and (2) total (both connected and isolated) porosity by small angle X-ray scattering. In summary, our evolving complementary approaches provide a rich toolbox for tackling the pore structure characteristics in geological barrier materials, and associated fluid flow & radionuclide transport, implicated in their long-term performance in natural and engineered systems of a nuclear waste repository.