Capillarity controls the distribution and transport of multiphase and immiscible fluids in soils and fractured rocks; therefore, capillarity affects the migration of nonaqueous contaminants and remediation strategies for both LNAPLs and DNAPLs, constrains gas and oil recovery, and regulates CO2 injection and geological storage. Surfactants alter interfacial tension and modify the invasion of pores by immiscible fluids. Experiments are conducted to explore the propagation of fluid interfaces along cylindrical capillary tubes and across pore constrictions in the presence of surfactants. Measured pressure signatures reflect the interaction between surface tension, contact angle, and the pore geometry. Various instabilities occur as the interface traverses the pore constriction, consequently, measured pressure signatures differ from theoretical trends predicted from geometry, lower capillary pressures are generated in advancing wetting fronts, and jumps are prone to under-sampling. Contact angle and instabilities are responsible for pronounced differences between pressure signatures recorded during advancing and receding tests. Pressure signatures gathered with surfactant solutions suggest changes in interfacial tension at the constriction; the transient surface tension is significantly lower than the value measured in quasi-static conditions. Interface stiffening is observed during receding fronts for solutions near the critical micelle concentration. Wetting liquids tend to form plugs at pore constrictions after the invasion of a nonwetting fluid; plugs split the nonwetting fluid into isolated globules and add resistance against fluid flow.