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Acridoidea is a superfamily within the Orthoptera order that comprises a group of short-horned insects commonly called grasshoppers. Grasshopper and locust species are major pests of grasslands and crops in all continents except Antarctica. Economically and historically, locusts and grasshoppers are two of the most destructive agricultural pests. The most important locust species belong to the genus Schistocerca and populate America, Africa, and Asia. Some grasshoppers considered to be important pests are the Melanoplus species, Camnula pellucida in North America, Brachystola magna and Sphenarium purpurascens in northern and central Mexico, and Oedaleus senegalensis and Zonocerus variegatus in Africa. Previous studies have classified these species based on specific characteristics. This review includes six headings. The first discusses the main species of grasshoppers and locusts; the second focuses on their worldwide distribution; the third describes their biology and life cycle; the fourth refers to climatic factors that facilitate the development of grasshoppers and locusts; the fifth discusses the action or reaction of grasshoppers and locusts to external or internal stimuli and the sixth refers to elements to design management strategies with emphasis on prevention.

Mathematical models allow for predictions of behavior under specific handling and environmental conditions, and are particularly useful in expensive studies or in studies where long term effects may be difficult to monitor. In mathematical modeling there are two main types of models: descriptive models and mechanistic models; the first are relationships between response and predictor which are not ruled by biological processes; the latter takes into account the basic processes in plants by means of differential equations to account for the development of plants. This requires a deeper knowledge of the physiological development of plants. This work reviews mathematical modeling on tomato plant. The TOMGRO model is modular and has been widely studied and calibrated under several climatic conditions which demonstrates that it is a robust model. As a future research the TOMGRO model is proposed to be adapted to other crops. Key words: Differential equations, descriptive models, mechanistic models.