  Future HEP experiments present stringent challenges to inorganic
scintillators in both fast timing response and radiation tolerance. This paper
reports recent progress in developing ultrafast inorganic scintillators with
sub-ns decay time for future precision timing detectors and high-rate
experiments. Performance of fast and ultrafast crystals with mass production
capability are compared to CsI crystals which are used for the Mu2e
calorimeter. Examples are LYSO:Ce, BaF2 and BaF2:Y, which are considered for
Mu2e-II. Crystal radiation hardness against gamma-rays and hadrons is reported.
Current status and development effort for the BaF2:Y crystals are discussed.
