We modeled the geometrical roughening of bedding-parallel, mainly layer-dominated stylolites in order to understand their structural evolution, to present an advanced classiﬁcation of stylolite shapes and to relate this classiﬁcation to chemical compaction and permeability variations at stylolites. Stylolites are rough dissolution seams that develop in sedimentary basins during chemical compaction. In the Zechstein 2 carbonate units, an important lean gas reservoir in the southern Permian Zechstein basin in Germany, stylolites inﬂuence local ﬂuid ﬂow, mineral replacement reactions and hence the permeability of the reservoir. Our simulations demonstrate that layer- dominated stylolites can grow in three distinct stages: an initial slow nucleation phase, a fast layer-pinning phase and a ﬁnal freezing phase if the layer is completely dissolved during growth. Dissolution of the pinning layer and thus destruction of the stylolite's compaction tracking capabilities is a function of the background noise in the rock and the dissolution rate of the layer itself. Low background noise needs a slower dissolving layer for pinning to be successful but produces ﬂatter teeth than higher background noise. We present an advanced classiﬁcation based on our simulations and separate stylolites into four classes: (1) rectangular layer type, (2) seismogram pinning type, (3) suture/sharp peak type and (4) simple wave-like type. Rectangular layer type stylolites are the most appropriate for chemical compaction estimates because they grow linearly and record most of the actual compaction (up to 40 mm in the Zechstein example). Seismogram pinning type stylolites also provide good tracking capabilities, with the largest teeth tracking most of the compaction. Suture/sharp peak type stylolites grow in a non-linear fashion and thus do not record most of the actual compaction. However, when a non-linear growth law is used, the compaction estimates are similar to those making use of the rectangular layer type stylolites. Simple wave-like stylolites are not useful for compaction estimates, since their growth is highly non- linear with a very low growth exponent. In the case where sealing material is collected at the tooth during dissolution, stylolites can act as barriers for local ﬂuid ﬂow as they intensify sealing capabilities of pinning layers. However, the development of teeth and spikes offsets and thus destroys continuous stylolite seams so that the permeability across the stylolite becomes very heterogeneous and they are no continuous barriers. This behavior is best shown in rectangular layer and seismogram pinning type stylolites that develop efﬁcient ﬂuid barriers at teeth tips but destroy sealing capabilities of layers by offsetting them at the ﬂank, leading to a permeability anisotropy along 2-D stylolite planes. Suture/sharp peak stylolites can create ﬂuid barriers if they collect enough sealing material. However, if the collecting material does not seal or if spikes offset the sealing material the stylolite leaks. We propose that our classiﬁcation can be used to realistically estimate chemical compaction in reservoirs and gives an indication on how heterogeneous the permeability of stylolites can be.