Let \(\Omega \subset \mathbb{R}^n, n\geq 2,\) be a bounded domain. A mapping \(f: \Omega \to \mathbb{R}^n\) in \(W^{1,1}(\Omega)\) is said to have a finite distortion if there exists a measurable function \(K(x)\geq 1\) such that \[ |Df(x)|\leq K(x) J(x,f) \quad\text{a.e.} \] These maps are currently under intensive research by many authors including the present authors. A guiding idea in these investigations is to determine to which extent Reshetnyak's theory of quasiregular mappings can be carried over to this case (in Reshetnyak's case \( K(x) \in L^{\infty}\) and \(f \in W^{1,n}_{\text{loc}}(\Omega)\)). It was recently proved by \textit{T. Iwaniec, P. Koskela}, and \textit{J. Onninen} [Invent. Math. 144, No. 3, 507-531 (2001; Zbl 1006.30016)] that if both \(\exp(\lambda K(x)) \in L^1(\Omega)\) for some \(\lambda>0\) and \(J(x,f) \in L^1(\Omega)\) then \(f\) is continuous. In the interesting paper under review the authors show that under these same hypotheses \(f\) is either constant or both discrete and open. Also many other results are proved and the sharpness of the results is studied.