Outline and shape reconstruction from unstructured points in a plane is a fundamental problem with many applications that has generated research interest for decades. Involved aspects like handling open, sharp, multiple and non-manifold outlines, run-time and provability as well as potential extension to 3D for surface reconstruction have led to many different algorithms. This multitude of reconstruction methods with quite different strengths and focus makes it a difficult task for users to choose a suitable algorithm for their specific problem. In this tutorial, we present proximity graphs, graph-based algorithms, algorithms with sampling guarantees, all in detail. Then, we show algorithms targeted at specific problem classes, such as reconstructing from noise, outliers, or sharp corners. Examples of the evaluation will show how its results can guide users to select an appropriate algorithm for their input data. As a special application, we show reconstruction of lines from sketches that can intersect themselves. Shape characterization of dot patterns will be shown as an additional field closely related to boundary reconstruction.