Hipparcos trigonometrical parallaxes of Mira-type variables have been combined with ground-based angular diameter measurements to derive linear diameters. Of eight stars with ground-based data, six have diameters indicating overtone pulsation whilst two, both with periods over 400 day, are pulsating in the fundamental. Hipparcos parallaxes of 11 Miras have been combined with extensive infrared photometry to determine the zero-point of the Mira period-luminosity relation. Adopting the relation at K (2.2 micron), since this is less likely to be subject to abundance effects than that at Mbol, leads to a distance modulus for the LMC of 18.6 mag with a uncertainty of slightly less than 0.2 mag. A brief discussion is given of the preliminary analysis of the parallaxes of a much larger sample of Miras. Some consideration is given to possible problems in interpreting the Hipparcos data which arise because of the physical characteristics of the Mira variables. Finally the apparent low-luminosity of the carbon Mira, R Lep, implied by the Hipparcos results leads to an interesting problem in AGB evolution.
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