Stellar-mass black holes and magentars have been identified by their bright non-thermal emissions. It is highly uncertain how these objects are formed, which is a missing link of massive stellar evolution. Newborn black holes and magnetars in collapsing massive stars have been considered as the central engine of e.g., gamma-ray bursts and superluminous supernovae. However, the event rates of such luminous transients are extremely small, say ~ 0.01 % of core-collapse supernovae. On the other hand, the formation rates of black holes and magnetars has been estimated to be possibly as high as ~10% of core-collapse supernovae. Thus, a large fraction of black-hole and magnetar formation would occur with ordinary supernovae or less prominent new transients. The key questions are "What are possible smoking guns of black-hole and mangetar formation?", "Whether they can be detectable by multi-messenger time-domain astronomy in the coming years?", and "What is the optimal observational strategy?". I will present some theoretical modeling of multi-messenger signals from newborn black holes and magnetars in collapsing massive stars and discussing the detectability by using current and future observational facilities.
