Einstein’s general relativity has passed enormous tests with flying colours, ranging from the Solar System, binary pulsars, gravitational waves, to cosmology. Binary pulsars, being in a strong-field regime with quasi-stationary orbital motion, are excellent testbeds for multiple aspects of gravitation. I will introduce the pulsar-timing techniques that have enabled the various tests, and highlight a few cases where binary pulsars have played an essential role, in particular where strong gravity has significantly impacted the inner structure of neutron stars. Using binary pulsars to test the universality of free fall and long-range fifth force from dark matters will be briefly introduced as well.