Local early-type galaxies (ETGs) are mostly populated by old stars, with little or no recent star formation activity. For this reason, they have historically been believed to be essentially devoid of cold gas, which is the fuel for the formation of new stars. Over the past two decades, however, increasingly-sensitive instrumentation observing the sky at (sub-)millimetre wavelengths has revealed the presence of significant amounts of cold molecular gas in the hearts of nearby ETGs. The unprecedented capabilities offered by the Atacama Large Millimeter/submillimeter Array (ALMA), in particular, have allowed us to obtain snapshots of the central regions of these ETGs with unprecedented detail, mapping this gas with higher sensitivity and resolution than ever before possible. Studies of the kinematics of the observed cold gas reservoirs are crucial for galaxy formation and evolution theories, providing, e.g., constraints on the fundamental properties and fuelling/feedback processes of super-massive black holes (SMBHs) at the centre of these galaxies. In this brief review, we summarise what the first 10 years of ALMA observations have taught us about the distribution and kinematics of the cold molecular gas component in nearby ellipticals and lenticulars.