Continuous monitoring of mechanical parameters determining the state of natural and manmade systems is essential in a wide range of engineering disciplines from mechanical to civil and geotechnical engineering. To be effective, the monitoring response time needs to be commensurate with the characteristic time of variation of the processes being monitored e.g. from seconds as for example in some machinery, to weeks and months for mining excavations and years in the case of structures. The

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... of measurement can therefore differ significantly for different applications. In spite of this, the methods of information processing-the computational monitoring-have considerable commonality. This review focuses on the methods of computational monitoring in solid and structural mechanics problems in different engineering applications. The traditional methods of monitoring are reviewed along with the corresponding computational and measurement methods. The basic principles of the computational monitoring in real time are established.