Pulsars are neutron stars which emit collimated beams of radio waves, observed as pulses, once per rotation of the neutron star. Due to evolutionary reasons, some pulsars behave as highly stable clocks and the measurement of the times of arrival of their pulses can provide an accurate determination of their positional, rotational and orbital parameters, as well as indications on the properties of their space- time environment. This in turn provides the observational basis for using the pulsars as magnificent tools for testing the gravity theories in a strong field regime. The talk will describe the experimental methodology for performing some of these tests, focusing on the Double pulsar system J0737-3039 ? i.e. the paradigmatic case for the class of tests involving binary pulsars - and on the case of the Pulsar Timing Array(s) ? i.e. the most promising approach for a direct detection of gravitational waves in the nano-Hz frequency range.