We present here an overview of the role of the multipolar black-body radiation (BBR) shifts in the single ion atomic clocks to appraise the anticipated 10−18 uncertainty level. With an attempt to use the advanced technologies for reducing the instrumental uncertainties at the unprecedented low, it is essential to investigate contributions from the higher-order systematics to achieve the ambitious goal of securing the most precise clock frequency standard. In this context, we have analysed contributions to the BBR shifts from the multipolar polarizabilities in a few ion clocks.