  We review our recent Michelson-Morley (MM) and Kennedy-Thorndike (KT)
experiment, which tests Lorentz invariance in the photon sector, and report
first results of our ongoing atomic clock test of Lorentz invariance in the
matter sector. The MM-KT experiment compares a cryogenic microwave resonator to
a hydrogen maser, and has set the most stringent limit on a number of
parameters in alternative theories to special relativity. We also report first
results of a test of Lorentz invariance in the SME (Standard Model Extension)
matter sector, using Zeeman transitions in a laser cooled Cs atomic fountain
clock. We describe the experiment together with the theoretical model and
analysis. Recent experimental results are presented and we give a first
estimate of components of the $\tilde{c}^p$ parameters of the SME matter
sector. A full analysis of systematic effects is still in progress, and will be
the subject of a future publication together with our final results. If
confirmed, the present limits would correspond to first ever measurements of
some $\tilde{c}^p$ components, and improvements by 11 and 14 orders of
magnitude on others.
