The crosier is the shepherd's staff, bent at the neck, used by bishops. It may be wood or metal.  Throughout history, Popes have not used the crosier.  Only since Paul VI have they used the pastoral staff.  The staff used by Popes in place of a crosier since Pope Paul VI (d. 1978) has been silver with a crucifix and corpus at the top.

The crosier is a symbol of the bishop's pastoral role. In the very early Church, it was constructed of rugged wood, but in the early Middle Ages wood was forbidden for bishops and was replaced by precious metal (silver and gold, depending on rank).  Wooden crosiers were again allowed 1400 years later by Pope Paul VI (d. 1978), and are common today.