  We study certain aspects of noncommutativity in field theory, strings and
membranes. We analyse the dynamics of an open membrane whose boundary is
attached to p-branes. Noncommutative features of the boundary string
coordinates are revealed by algebraic consistency arguments. Next, we derive
Seiberg-Witten-type maps relating currents and their divergences in nonabelian
U(N) noncommutative gauge theory with the corresponding expressions in the
ordinary (commutative) description. We then exploit these maps to obtain the
O(\theta) structure of the commutator anomalies in noncommutative
electrodynamics. Finally, we discuss the issue of violation of Lorentz
invariance in noncommutative gauge theories by explicitly deriving, following a
Noether-like approach, the criteria for preserving Poincare invariance. We also
study general (deformed) conformal-Poincare (Galilean) symmetries consistent
with relativistic (nonrelativistic) canonical noncommutative spaces.
