Let $R$ be the ring of integers in an algebraic number field. There are beautiful descriptions of $K_0(R)$ and $K_1(R)$. Namely, $K_0(R)$ is the class group of $R$ and $K_1(R)$ is the group of units of $R$. Question : Is there a nice description of $K_2(R)$ (or at least some reasonable conjectures)? I couldn't find much about this in Milnor's or Rosenberg's books on algebraic K-theory, so I expect that the answer is pretty complicated. Is it maybe at least known in some special cases (say, for $R$ the integers in a quadratic extension of $\mathbb{Q}$)?

Let $R$ be the ring of integers in an algebraic number field. There are beautiful descriptions of $K_0(R)$ and $K_1(R)$. Namely, $\tilde{K}_0(R)$ is the class group of $R$ and $K_1(R)$ is the group of units of $R$. Question : Is there a nice description of $K_2(R)$ (or at least some reasonable conjectures)? I couldn't find much about this in Milnor's or Rosenberg's books on algebraic K-theory, so I expect that the answer is pretty complicated. Is it maybe at least known in some special cases (say, for $R$ the integers in a quadratic extension of $\mathbb{Q}$)?