A summary is given of research on transient (duration $\approx$10$^{-1}$--10$^{-2}$ sec) bursts of cosmic $\gamma$ rays monitored with spacecraft carrying special-purpose detectors. Very likely the burst sources are old (>10$^6$ yr) magnetized neutron stars located fairly close to the solar system (D$\approx$10--100 pc). A most interesting physical problem thereby awaits investigation: the nonstable behavior of ultradense matter in strong magnetic fields (B$\approx$10$^{12}$--10$^{13}$ gauss). Several nonstable processes that might generate the observed bursts are discussed.