Highly mismatched alloys (HMAs) is a class of semiconductor alloys whose constituents are distinctly different in terms of size, ionicity and/or electronegativity. Electronic properties of the alloys deviate significantly from an interpolation scheme based on small deviations from the virtual crystal approximation. Most of the HMAs were only studied in a dilute composition limit. Recent advances in understanding of the semiconductor synthesis processes allowed growth of thin films of HMAs under non-equilibrium conditions. Thus reducing the growth temperature allowed synthesis of group III-N-V HMAs over almost the entire composition range. This paper focuses on the GaNxSb1-x HMA which has been suggested as a potential material for solar water dissociation devices. Here we review our recent work on the synthesis, structural and optical characterization of GaN1-xSbx HMA. Theoretical modeling studies on its electronic structure based on the band anticrossing (BAC) model are also reviewed. In particular we discuss the effects of growth temperature, Ga flux and Sb flux on the incorporation of Sb, film microstructure and optical properties of the alloys. Results obtained from two separate MBE growths are directly compared. Our work demonstrates that a large range of direct bandgap energies from 3.4 eV to below 1.0 eV can be achieved for this alloy grown at low temperature. We show that the electronic band structure of GaN1-xSbx HMA over the entire composition range is well described by a modified the BAC model which includes the dependence of the host matrix band edges as well as the BAC model coupling parameters on composition. We emphasize that the modified BAC model of the electronic band structure developed for the full composition of GaNxSb1-x is general and is applicable to any HMA.