Purely non-inductive steady-state discharges in tokamak reactors will require a large bootstrap current, I-boot, in order to minimize the amounts of power in external current drive systems. in present day tokamaks, high bootstrap current discharges are produced under various conditions. It has been demonstrated that the on-axis RF heatings are good candidates for producing a large bootstrap current, especially the fast magnetosonic wave direct electron heating (FWEH), for which power deposition is centrally peaked. Moreover, the heating and current drive methods using RF waves could be used as external sources to optimize I-boot through the current profile control. In this paper, the dependence of I-boot on the profiles of the plasma density, temperature, pressure and current density is analysed using a theoretical approach with a matrix formulation. Examples of quasi-steady-state discharges with large bootstrap current fraction using FWEH on Tore Supra are given. Examples of high bootstrap current fractions on reverse shear discharges (TFTR, DIII-D,...) are also mentioned. Purely non-inductive discharges with improved confinement by combination of FWEH and lower hybrid current drive are analysed and the extrapolation to the so-called 'Tore Supra CIEL phase' is reported.