Abstract
Three issues, which are to my opinion the main obstacles in modeling the variability of Miras and Long Period Variables (LPVs), are presented and discussed: a.The initial static models - Possible influences of the evolutionary details, the helium shell flashes and the use of the core-mass luminosity relation.b.Modeling the convective energy transport - The mixing-length theory, its limitations and validity. First attempts for two-dimensional calculations of the convective flow in AGB stars.c.The surface conditions - Introduction to the main difficulties and uncertainties. What should be done in the future.Finally, the ancient problem, concerning the mode of pulsation, in Miras, is discussed using the recent radii observations confronted with the results of our full non-linear calculations.
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