This review discusses the study of thermal conduction in classical low-dimensional lattices, focusing on the breakdown of Fourier's law and the role of lattice dimensionality. It presents various models, including harmonic and anharmonic chains, and explores the behavior of heat transport in both equilibrium and non-equilibrium conditions. The paper examines the role of disorder, localization, and the effects of external potentials on thermal conductivity. It also discusses the traditional kinetic approach based on the Boltzmann-Peierls equation and the Green-Kubo formula, as well as mode-coupling theory. The review highlights the divergence of thermal conductivity in one and two dimensions and the importance of understanding the underlying mechanisms of heat transport in low-dimensional systems. It also addresses the use of stochastic and deterministic baths in simulating thermal transport and the comparison of different methods for modeling heat baths. The paper emphasizes the importance of understanding the universality of quantitative data and the role of ergodicity in ensuring normal heat transport. It concludes with a discussion of open questions and future research directions in the field of thermal conduction in low-dimensional lattices.This review discusses the study of thermal conduction in classical low-dimensional lattices, focusing on the breakdown of Fourier's law and the role of lattice dimensionality. It presents various models, including harmonic and anharmonic chains, and explores the behavior of heat transport in both equilibrium and non-equilibrium conditions. The paper examines the role of disorder, localization, and the effects of external potentials on thermal conductivity. It also discusses the traditional kinetic approach based on the Boltzmann-Peierls equation and the Green-Kubo formula, as well as mode-coupling theory. The review highlights the divergence of thermal conductivity in one and two dimensions and the importance of understanding the underlying mechanisms of heat transport in low-dimensional systems. It also addresses the use of stochastic and deterministic baths in simulating thermal transport and the comparison of different methods for modeling heat baths. The paper emphasizes the importance of understanding the universality of quantitative data and the role of ergodicity in ensuring normal heat transport. It concludes with a discussion of open questions and future research directions in the field of thermal conduction in low-dimensional lattices.