In recent years many experimentalists have reported an anomalously enhanced thermal conductivity in liquid suspensions of nanoparticles. Despite the importance of this effect for heat transfer applications, no agreement has emerged about the mechanism of this phenomenon, or even about the experimentally observed magnitude of the enhancement. To address these issues, this paper presents a combined experimental and theoretical study of heat conduction and particle agglomeration in nanofluids. On the experimental side, nanofluids of alumina particles in water and ethylene glycol are characterized using thermal conductivity measurements, viscosity measurements, dynamic light scattering, and other techniques. The results show that the particles are agglomerated, with an agglomeration state that evolves in time. The data also show that the thermal conductivity enhancement is within the range predicted by effective medium theory. On the theoretical side, a model is developed for heat conduction through a fluid containing nanoparticles and agglomerates of various geometries. The calculations show that elongated and dendritic structures are more efficient in enhancing the thermal conductivity than compact spherical structures of the same volume fraction, and that surface (Kapitza) resistance is the major factor resulting in the lower than effective medium conductivities measured in our experiments. Together, these results imply that the geometry, agglomeration state, and surface resistance of nanoparticles are the main variables controlling thermal conductivity enhancement in nanofluids.