After the Buddha reached Parinirvāṇa (he passed away) his body was cremated. The remaining ashes and pieces of bone where distributed amongst his most influential followers.
The relics spread across south-east Asia. For example to the Buddha Tooth Relic Temple in Singapore.
I’ve seen relics in a museum in Kolkata, India in 2005 and most recently in the National Museum in New Delhi.
The relics in the National Museum are displayed in an ornate golden stūpa-like structure. The bone fragments are within a glass dome towards the top of the structure on a small pedestal. The whole stūpa is kept behind glass. Originally the bones were found in small clay pots in a larger stūpa that was destroyed. Two of these clay pots are within the same display.
Pilgrims visiting New Delhi flock to the National Museum to see the relics, circumambulate the little shrine and in some occasions sit down and offer pūjas (sung meditation), whilst others find a silent corner and contemplate/meditate quietly in the presence of the bone relics and absorb the blessing. The museum prohibits physical offerings of any kind.