In the hopes of helping the discovery of a really biaxial nematic phase in the thermotropic liquid crystal family, we give a brief review on the experimental methods available for proving biaxiality in oriented or disoriented samples. We discuss the relative advantages and problems that arise with the biaxial tests based on the NMR techniques, X-ray and neutron scatterings, dynamic modes analysis, inspection of defects, or the determination of coupling constants as in conoscopy. Among these different methods, two, conoscopy and defects analysis, seem particularly useful since they may be really conclusive without excessive sophistications. They may therefore be recommended as tests for biaxiality. Conoscopy is most probably the safest way to prove biaxiality, but it needs perfectly oriented samples. In order to warrant that the samples are indeed correctly oriented, the conoscopic patterns should be observed with several entire and well-contrasted rings. Conversely, if the rings are incomplete or fading somewhere, the observed biaxiality is only apparent and likely to be produced by orientation gradients. The analysis of the disclination lines may also be used with benefit to prove biaxiality. One should then carefully control the width and contrast of the lines to keep them sharp and regular all along, in order not to confuse them with mirages. To prove biaxiality, at least two types of disclination lines should be observed with typical variations of the zigzag angles, contrasts and relaxation rates as functions of temperature.