Lethal damage and effects that say “destroy” won’t cause a permanent with indestructible to be put into the graveyard. However, a permanent with indestructible can be put into the graveyard for a number of reasons. The most likely reasons are if it’s sacrificed, if it’s a creature whose toughness is 0 or less, or if it’s an Aura that’s either unattached or attached to something illegal.