Factorization algebras are algebraic structures which encode the structure of the observables of a (perturbative) quantum field theory. Examples include (homotopy) algebras and (pointed) bimodules, but also braided monoidal categories such as the category of finite dimensional representations of a reductive algebraic group Rep G or of the associated quantum group Rep U_q(g), and, coming from topology, E_n-algebras, which are algebras for the little disks operad. They can be thought of as a multiplicative version of a cosheaf and thus provide a geometric way of thinking about algebraic objects. After discussing some examples, I will explain how one can use geometric ideas and intuition for algebraic results. Then I will outline a program of how to relate factorization algebras to a different axiomatic approach to quantum field theory, namely, functorial field theories.