Let $M$ be an injective factor with separable predual. Then the type I possibilities are the usual full operator algebras $M_n(\mathbb C)$ and $\mathcal{L}(H)$, with $H$ separable in the type $I_\infty$ case. There is a unique injective type $II_1$ factor, the hyperfinite factor $R$, and a unique injective type $II_\infty$ factor, $R\overline{\otimes}\mathcal{L}(\ell^2(\mathbb N))$. In type III, the injective factors with separable predual are classified by the Connes-Haagerup invariants: the parameter $\lambda\in[0,1]$ for types $III_\lambda$ with $0<\lambda\le 1$, together with the flow of weights in the type $III_0$ case.