A covariant formalism is presented to describe the dynamics of an arbi
trary membrane with smooth physical boundaries. We exploit the fact th
at the boundary worldsheet is an embedded surface of codimension one i
n the worldsheet spanned by the membrane in spacetime. The formalism a
pplies to any effective theory for the dynamics of the membrane and of
its boundary. The case of extremal membranes with extremal boundaries
is discussed in detail.