The positive ion chemistry of H3BO3 has been studied by chemical ionization (CI) and Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry. From the results of equilibrium and "bracketing" experiments, the gas-phase basicity (GPB) and the proton affinity (PA) of H3BO3 are estimated to be 167.8 +/- 0.5 and 176 +/- 2 kcal mol-1 respectively. The latter value is in fair agreement with the PA of 181.2 kcal mol-1 from MO SCF calculations at the MP3/6-31G**//6-31G* + ZPVE (6-31G*) level of theory. The PA of HBO2 calculated at the MP4(SDTQ)/6-31G**//6-31G* + ZPVE (6-31G*) level is 181.2 kcal mol-1, which falls within the interval set by ICR "bracketing" experiments. The H4BO3+ ion undergoes condensation with H3BO3 yielding protonated polyboric acids containing up to seven B atoms belonging to three different classes, (Hn+2BnO2n+1)H+, (HnBnO2n)H+ and (Hn-2BnO2n-1)H+, formed via sequences established by FT-ICR experiments involving isolation of the ionic reactants by multiple resonance. The structures of the polyions observed are discussed and compared to those of the corresponding anions, also observed in the gas phase, and of the few anions whose structures have been established in crystalline borates. The fast isotope exchange with (H2O)-O-18 undergone by H4BO3+ suggests that the H6BO4+ ion observed in the CI spectra of H3BO3 may contain a tetrahedrally coordinated B atom, as present in many borate and polyborate anions. The reactions of H3BO3 and/or of H4BO3+ with MeOH and HCOOH, yielding protonated esters, respectively anhydrides, of boric and polyboric acids are surveyed.