The effect of the microwave-assisted acid treatment (MAT) on the structure and texture of dioctahedral (montmorillonite) and trioctahedral (saponite) smectites, kerolitic clays and sepiolites were studied by scanning electron microscopy, nitrogen adsorption, X-ray fluorescence, X-ray diffraction and Fourier transform infrared spectroscopy. This study shows that in the smectite group of minerals the effectiveness of MAT is notably influenced by the chemical composition of the octahedral sheet, whereas in kerolitic clays it is influenced by the proportion of the expandable phase in the mixed layer sequence. On the other hand, the reactivity of sepiolites depends on the width of the natural fibres. With these treatments, extremely high specific surface area (SSA) increments are achieved in just 16 min. The SSA increments reach values up to 231 m2/g (%ΔSBET = 80) in sepiolites, 198 m2/g (%ΔSBET = 155) in Mg-smectites, and 161 m2/g (%ΔSBET = 61) in kerolitic clays.