The article is a brief review on the potential of transmission electron microscopy (ТЕМ) in the investigation of atom chains which are the paradigm of a strictly one-dimensional material. After the progress of ТЕМ in the study of new two-dimensional materials, microscopy of free-standing one-dimensional structures is a new challenge with its inherent potentials and difficulties. In-situ experiments in the ТЕМ allowed, for the first time, to generate isolated atomic chains consisting of metals, carbon, or boron nitride. Besides having delivered a solid proof for the existence of atomic chains, in-situ ТЕМ studies also enabled us to measure the electrical properties of these fundamental linear structures. While ballistic quantum conductivity is observed in chains of metal atoms, electrical transport in chains of spJ-hybridized carbon is limited by resonant states and reflections at the contacts. Although substantial progress has been made in recent ТЕМ studies of atom chains, fundamental questions have to be answered, concerning the structural stability of the chains, bonding states at the contacts, and the suitability for applications in nanotechnology.