High quality single crystals of both Pb-free and Pb-doped Bi-2223 (with sizes up to 3×2×0.1mm<sup>3</sup>) were grown by means of a newly developed "Vapor-Assisted Travelling Solvent Floating Zone" technique in an image furnace. This technique allowed us to grow large Pb-doped Bi-2223 crystals for the first time. Post-annealing in high pressure oxygen (up to 10 MPa) enhanced T<sub>c</sub> (up to 111 K) and sharpened the superconducting transition. The crystal structures of both Bi-2223 and Bi,Pb-2223 were refined and are reported in this paper. The unit cell of the Pb-free average structure is pseudo-tetragonal with a=5.4210(7), b=5.4133(6) and c=37.009(7) Å. An incommensurate structural modulation along the direction of one of the short cell vectors has been defined (q∼0.21 a<sup>*</sup>); however, the structure can be conveniently described in a supercell with a 5-fold volume (a=27.105(4) Å). One additional O atom per translation unit of the modulation wavelength was found to be inserted into the BiO layers. Approximately 8% of the Ca sites are occupied by Bi atoms, and the refined composition is found to be Bi:Sr:Ca:Cu:O=2.16:2:1.84:3:10.16. Similar features are found in the Pb-doped phase. The magnetization of Pb-free Bi-2223 crystals has been studied. The vortex phase diagram has been traced and the anisotropy of Bi-2223 is found to be γ=53 from measurements of the lower critical field, which is much smaller than that of Bi-2212 (γ=165). Bi-2223 has a higher critical current density, and a reduced magnetic relaxation rate compared to Bi-2212, both of which are signatures of more effective pinning in Bi-2223 due to its reduced anisotropy.