Within the currently rising trend of heterogeneous microsystem integration and packaging, capillary self-assembly emerges as an innovative technique to enhance, complement and eventually replace pick-and-place assembly. Vast literature and experimental data support such claim. Still, the technique needs to overcome some important limitations in order to fully express its potential and earn wide industrial recognition. In this paper, we review and illustrate what are in our opinion the challenges ahead for making part-to-substrate capillary self-assembly reliable and seriously competitive with long-established assembly techniques. After setting self-assembly methods in the context of microsystem assembly and integration technologies, we focus on the standard embodiment of capillary self-assembly, and we describe in details the main, often novel technological steps required for its effective and reproducible performance. This preludes to an outline of what are presently, in our view, the major failure modes affecting the overall yield of the capillary self-assembly technique. Consequently, we propose solutions to face and overcome these challenges, which need to be met to foster the success of this technique.