This paper reviews the thermal conduction in classical low-dimensional lattices, focusing on the role of lattice dimensionality on the breakdown of Fourier's law. The authors derive macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models consisting of coupled oscillators on a lattice. They emphasize universal quantitative aspects, such as the divergence of finite-size thermal conductivity in one and two dimensions. The paper covers various topics, including heat baths, harmonic systems, linear response theory, anharmonic chains, integrability, and ballistic transport. It also discusses the behavior of two-dimensional lattices and outlines future research directions. The authors use both analytical and numerical methods to investigate thermal conduction, providing a comprehensive overview of the field.This paper reviews the thermal conduction in classical low-dimensional lattices, focusing on the role of lattice dimensionality on the breakdown of Fourier's law. The authors derive macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models consisting of coupled oscillators on a lattice. They emphasize universal quantitative aspects, such as the divergence of finite-size thermal conductivity in one and two dimensions. The paper covers various topics, including heat baths, harmonic systems, linear response theory, anharmonic chains, integrability, and ballistic transport. It also discusses the behavior of two-dimensional lattices and outlines future research directions. The authors use both analytical and numerical methods to investigate thermal conduction, providing a comprehensive overview of the field.