Many species of insect pests can be detected and monitored automatically. Several systems have been designed in order to improve integrated pest management (IPM) in the context of precision agriculture. Automatic detection traps have been developed for many important pests. These techniques and new technologies are very promising for the early detection and monitoring of aggressive and quarantine pests. The aim of the present paper is to review the techniques and scientific state of the art of the use of sensors for automatic detection and monitoring of insect pests. The paper focuses on the methods for identification of pests based in infrared sensors, audio sensors and image-based classification, presenting the different systems available, examples of applications and recent developments, including machine learning and Internet of Things. Future trends of automatic traps and decision support systems are also discussed.