Understanding phonon heat conduction mechanisms in low-dimensional structures is of critical importance for low-dimensional thermoelectricity. In this paper, we discuss heat conduction mechanisms in two-dimensional (2D) and one-dimensional (1D) structures. Models based on both the phonon wave picture and particle picture are developed for heat conduction in 2D superlattices. The phonon wave model, based on the acoustic wave equations, includes the effects of phonon interference and tunneling, while the particle model, based on the Boltzmann transport equation, treats the internal as well interface scattering of phonons. For 1D systems, both the Boltzmann transport equation and molecular dynamics simulation approaches are employed. Comparing the modeling results with experimental data suggest that the interface scattering of phonons plays a crucial role in the thermal conductivity of low-dimensional structures. We also discuss the minimum thermal conductivity of low-dimensional structures based on a generalized thermal conductivity integral, and suggest that the minimum thermal conductivities of low-dimensional systems may differ from those of their corresponding bulk materials. The discussion leads to alternative ways to reduce thermal conductivity based on the propagating phonon modes.