Overhead power transmission lines, their supporting towers, insulators and other elements create a highly distributed system that is vulnerable to damage. Typical damage scenarios cover cracking of foundation, breakage of insulators, loosening of rivets, as well as cracking and breakage of lines. Such scenarios may result from various factors: groundings, lightning strikes, floods, earthquakes, aeolian vibrations, conductors galloping, icing, and also include sabotage or terrorist attacks. It is impossible to monitor every kilometer of power lines, especially when they pass through inaccessible areas like mountains or swamps. This implies that many of the damage scenarios mentioned remain unnoticed or are detected too late. In most cases damage of the power system leads to instantaneous blackouts of small regions, but huge blackouts are also possible. Every power outage causes a great financial loss, threats to hospital patients, public transport or even national security. The paper presents a brief introduction to the field of damage detection in transmission towers, emphasizing indexes calculated by simple processing and using artificial neural networks. Problem of line sag monitoring is also mentioned. The paper ends with a short report on possible financial impacts of an SHM system for electric energy transmission and distribution system.