  In this paper, we review tests of the strong equivalence principle (SEP)
derived from pulsar-white dwarf data. The extreme difference in binding energy
between both components and the precise measurement of the orbital motion
provided by pulsar timing allow the only current precision SEP tests for
strongly self-gravitating bodies. We start by highlighting why such tests are
conceptually important. We then review previous work where limits on SEP
violation are obtained with an ensemble of wide binary systems with small
eccentricity orbits. Then we propose a new SEP violation test based on the
measurement of the variation of the orbital eccentricity de/dt. This new method
has the following advantages: a) unlike previous methods it is not based on
probabilistic considerations, b) it can make a direct detection of SEP
violation, c) the measurement of de/dt is not contaminated by any known
external effects, which implies that this SEP test is only restricted by the
measurement precision of de/dt. In the final part of the review, we
conceptually compare the SEP test with the test for dipolar radiation damping,
a phenomenon closely related to SEP violation, and speculate on future
prospects by new types of tests in globular clusters and future triple systems.
