Stylolites are among the most prominent features in compacted and deformed limestones. They appear as dark lines in the rock and have a distinct geometry showing roughness on several scales and structures that are known as teeth. A stylolite is a plane of localized dissolution where the development of the roughness is induced by the collection of slower dissolving particles within the stylolite. In this contribution we show with a numerical model how a stylolite roughens with time. We will illustrate with a number of movies of stylolite growth how these structures develop in detail and how the growth changes from small to large scale. We will explore stylolite-growth using scaling methods from statistical physics and show how the growth changes depending on the scale of the system but also on the nature and size of the noise that induces the roughening. Finally a simulation with a large-scale noise sitting on large grains and a small-scale noise in the background will be used to show how stylolites grow in a rock that contains fossils or large ooids.