The complexity of application landscapes (AL) has been identified as one of the major challenges in enterprise architecture (EA) management for quite some time. Since there is no agreed upon definition of the term complexity in general or in the context of EA management in particular, literature offers a broad variety of concepts and measurements. Therefore, the main purpose of this paper is to (1) provide an overview about metrics to quantify the complexity of ALs proposed in literature, (2) identify metrics currently used in practice to measure AL complexity, and (3) compare empirical results and assess the metrics’ applicability with industry experts. By the assessment of four different ALs from the financial sector, we are able to derive various strengths and weaknesses for the different metrics as well as open issues for future research on quantitative EA models.