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According to general relativity, a spinning body of mass M and angularmomentum S, like a star or a planet, generates a gravitomagnetic field whichinduces, among other phenomena, also the Lense-Thirring effect, i.e. secularprecessions of the path of a test particle orbiting it. Direct and indisputabletests of such a relativistic prediction are still missing. We discuss someperformed attempts to measure it in the gravitational fields of several bodiesin the Solar System with natural and artificial objects. The focus is on therealistic evaluation of the impact of some competing classical forces regardedas sources of systematic uncertainties degrading the total accuracy obtainable.

Recent Attempts to Measure the General Relativistic Lense-Thirring Effect with Natural and Artificial Bodies in the Solar System