  We prove that every 2-local derivation from the algebra
$M_n(\mathcal{A})(n>2)$ into its bimodule $M_n(\mathcal{M})$ is a derivation,
where $\mathcal{A}$ is a unital Banach algebra and $\mathcal{M}$ is a unital
$\mathcal{A}$-bimodule such that each Jordan derivation from $\mathcal{A}$ into
$\mathcal{M}$ is an inner derivation, and that every 2-local derivation on a
C*-algebra with a faithful traceable representation is a derivation. We also
characterize local and 2-local Lie derivations on some algebras such as von
Neumann algebras, nest algebras, Jiang-Su algebra and UHF algebras.
