Several organic and inorganic materials have emerged as promising candidates for the active layer of field-effect transistors (FETs) fabricated on flexible substrates. The charge transport models necessary for device optimization in these systems are at different stages of development. The understanding of charge transport in single-crystal and thin-film FETs based on organic materials such as pentacene, rubrene, and other related compounds has advanced considerably in recent years and a clear picture of the relevant transport mechanisms is forming. In contrast, the theoretical description of transport in hydrogenated microcrystalline silicon (mu c-Si:H) is not as well known and the published results and theories are often contradictory. We review the paradigms we feel are useful in describing the cur-rent understanding of transport in organic and mu c-Si:H field-effect transistors. In the case of organic materials these include the polarization and transfer integral fluctuation model [A. Troisi and G. Orlandi, Phys. Rev. Lett. 96, 086601 (2006), J.-D. Picon et al., Phys. Rev. B 75, 235106 (2007)], the Frolich polaron model [I.N. Hulea el al., Nat. Mater. 5, 982 (2006), H. Houilli et al., J. Appl. Phys. 100, 033702 (2006)], and several trapping models [M.E. Gershenson et al., Rev. Mod. Phys. 78, 973 (2006), V. Podzorov et al., Phys Rev. Lett. 95, 226601 (2005)]. Given the heterogeneous composition and structure of microcrystalline silicon thin films, a variety of theories to describe dark conductivity have been applied to mu c-Si:H including those based on percolation theory [H. Overhof et al., J. Non-Cryst. Solids 227-230, 992 (1998)], hopping models [A. Dussan and R. H. Buitrago, J. Appl. Phys. 97, 043711 (2005)], thermionic emission, and tunneling. We give a brief overview of these models and present a fluctuation-induced tunneling model that we are developing to describe charge transport in microcrystalline silicon.