This review article, authored by Nicolás Agraït, Alfredo Levy Yeyati, and Jan M. van Ruitenbeek, explores the quantum properties of atomic-sized conductors, focusing on the electrical and mechanical properties of metallic contacts at the atomic scale. The authors discuss the experimental techniques used to study these properties, including the use of scanning tunneling microscopes (STM) and the mechanically controllable break junction (MCBJ) technique. They highlight the importance of mesoscopic physics in understanding the behavior of these systems, where quantum effects become significant due to the small size of the contacts. The review covers a range of topics, including the fabrication of metallic point contacts, the theoretical models for transport properties, and the experimental observations of conductance quantization, shot noise, and dynamical Coulomb blockade. It also discusses the mechanical properties of atomic-sized contacts, such as elastic and plastic deformations, and the formation of conducting chains of individual atoms. Key findings include the discovery of conductance quantization in atomic-sized contacts, the role of multiple Andreev reflection in superconducting point contacts, and the unusual mechanical behavior of gold contacts, which can form stable conducting chains. The authors also review the use of computer simulations to understand the structural evolution and cohesive forces in atomic-scale contacts. The review concludes with a discussion of future research directions, emphasizing the importance of combining theoretical and experimental approaches to further our understanding of the complex behavior of atomic-sized conductors.This review article, authored by Nicolás Agraït, Alfredo Levy Yeyati, and Jan M. van Ruitenbeek, explores the quantum properties of atomic-sized conductors, focusing on the electrical and mechanical properties of metallic contacts at the atomic scale. The authors discuss the experimental techniques used to study these properties, including the use of scanning tunneling microscopes (STM) and the mechanically controllable break junction (MCBJ) technique. They highlight the importance of mesoscopic physics in understanding the behavior of these systems, where quantum effects become significant due to the small size of the contacts. The review covers a range of topics, including the fabrication of metallic point contacts, the theoretical models for transport properties, and the experimental observations of conductance quantization, shot noise, and dynamical Coulomb blockade. It also discusses the mechanical properties of atomic-sized contacts, such as elastic and plastic deformations, and the formation of conducting chains of individual atoms. Key findings include the discovery of conductance quantization in atomic-sized contacts, the role of multiple Andreev reflection in superconducting point contacts, and the unusual mechanical behavior of gold contacts, which can form stable conducting chains. The authors also review the use of computer simulations to understand the structural evolution and cohesive forces in atomic-scale contacts. The review concludes with a discussion of future research directions, emphasizing the importance of combining theoretical and experimental approaches to further our understanding of the complex behavior of atomic-sized conductors.