Let $A$ and $B$ be $C^{\ast}$-algebras. It is well known that maximal tensor product of simple $C^{\ast}$-algebra need not be simple. So basically the ideal structure of $A\otimes_{max}B$ does not really depends on ideal structure of $A$ and of $B$.

What is known about ideals of $A\otimes_{max}B$ .

Any references?