We present results of integral field optical spectroscopy of five luminous blue compact dwarf galaxies. The data were obtained using the fiber system INTEGRAL attached to the William Herschel Telescope. The galaxies Mrk 370, Mrk 35, Mrk 297, Mrk 314, and III Zw 102 were observed. The central 33.6''×29.4'' regions of the galaxies were mapped with a spatial resolution of 2.7" spaxel-1, except for Mrk 314, in which we observed the central 16''×12'' region with a resolution of 0.9" spaxel-1. We use high-resolution optical images to isolate the star-forming knots in the objects; line ratios, electron densities, and oxygen abundances in each of these regions are computed. We build continuum and emission-line intensity maps, as well as maps of the most relevant line ratios: [O III] λ5007/Hβ, [N II] λ6584/Hα, and Hα/Hβ, which allow us to obtain spatial information on the ionization structure and mechanisms. We also derive the gas velocity field from the Hα and [O III] λ5007 emission lines. We find that all five galaxies are in the high end of the metallicity range of blue compact dwarfs with oxygen abundances varying from Z~=0.3 to 1.5 Zsolar. The objects show H II-like ionization in the whole field of view, except the outer regions of III Zw 102, whose large [N II] λ6584/Hα values suggest the presence of shocks. The five galaxies display inhomogeneous extinction patterns, and three of them have high Hα/Hβ ratios, indicative of a large dust content; all of the galaxies display complex, irregular velocity fields in their inner regions.