For more than a decade, a group at the University of Florida has been constructing models of barred spiral galaxies that we have observed at the VLA. Group members include: S. T. Gottesman, G. Contopoulos, J. H. Hunter, several Ph.D. students, and collaborators at other institutions. The HI distributions in our galaxies are either gas rich, or nearly devoid of gas, in their bar regions. Initially, we deduced density distributions and potentials of the stellar disks and bars from near infrared observations, modeled the gas response assuming different pattern speeds, etc., and compared the models with our HI observations. This simple approach is successful in some cases, such as NGC 3359, but less successful in others. More recently, our approach has been toward selfconsistent models, including stars and gas. Our techniques range from the Contopoulos-Grosbøl-Kaufmann stellar dynamical approach to methods exploiting grid codes and SPH tree codes. Some of our observations and models will be reviewed, and some new results will be presented.