Identifying urban boundaries involves analysing both the functional and the morphological aspects of urban systems. In this paper, we adopt a purely morphological approach and compare three methods for the morphological delineation of cities. Each method avoids using any predefined quantified threshold (size, distance, built density, etc.) to detect crucial discontinuities in space. The first method identifies Natural Cities by clustering points. The other two are the fractal-based MorphoLim method and the Hierarchical Percolation; both involve transforming the data using a step-by-step dilation process. The three methods are critically compared and illustrated by applications to theoretical urban patterns. We further apply each method to the urban agglomeration of Brussels, the Belgian capital, using different data (building footprints, building centroids and street nodes) and considering two study areas, namely the former province of Brabant and the entire country of Belgium. The results show that it is impossible to draw an unambiguous morphological boundary for an urban agglomeration. Consequently, it is crucial to relate the data used, the size of the study area and the method chosen to the objectives of the delineation.