  According to general relativity, a spinning body of mass M and angular
momentum S, like a star or a planet, generates a gravitomagnetic field which
induces, among other phenomena, also the Lense-Thirring effect, i.e. secular
precessions of the path of a test particle orbiting it. Direct and indisputable
tests of such a relativistic prediction are still missing. We discuss some
performed attempts to measure it in the gravitational fields of several bodies
in the Solar System with natural and artificial objects. The focus is on the
realistic evaluation of the impact of some competing classical forces regarded
as sources of systematic uncertainties degrading the total accuracy obtainable.
