We describe briefly some results obtained on both chiral and achiral compounds exhibiting chiral mesophases. We report the first example of a single component system exhibiting the undulated twist grain boundary C Ã or UTGB C Ã phase. Preliminary results concerning a few achiral compounds composed of banana-shaped molecules exhibiting a mesophase is reported. They have been investigated by polarized light optical microscopy, differential scanning calorimetry and x-ray diffraction studies.