The construction of the Terawatt Accumulator (TWAC) facility is nearly completed at the ITEP in Moscow. All the major milestones have been successfully passed with a beam of carbon ions, except for the final result (the high power beam accumulation), which is on the way. The beam of C4+ ions delivered by the laser ion source is accelerated up to the energy of 300 MeV/amu by two steps—in the linear injector I3 and in the booster synchrotron UK. The accelerated beam is extracted from the UK ring and transferred to the U10 accumulator ring. Non-Liouvillian stripping technique (C4+ ⇒ C6+) is applied for stacking of C6+ batches into the accumulator ring U10. First experiments with extracted beam of ions have started in 2002. Status of the TWAC components, current results of activities aiming at mastering the ion beam stacking technique, and outlook for the TWAC advance are presented.