An integer distance graph is a graph \(G(D)\) with vertex set the set \(\mathbb{Z}\) of integers and two vertices \(u,v\in \mathbb{Z}\) adjacent if and only if \(|u-v|\in D\), where the distance set \(D\) is a subset of the set of positive integers \(\mathbb{N}\). In this paper the chromatic index, the choice index, the total chromatic number and the total choice number of all integer distance graphs, and the choice number of special integer distance graphs are determined. Most of them are equal to \(2|D|\) or to \(2|D|+1\).