Different phenomena related to the spontaneous accumulation of solid particles dispersed in a fluid medium in microgravity conditions are discussed, with an emphasis on recent discoveries and potential links with the general field of astrophysical fluid-dynamics on the one hand, and with terrestrial applications in the field of materials science on the other hand. With special attention to the typical physical forces at play in such an environment, namely, surface-tension gradients, oscillatory residual gravity components, inertial disturbances and forces of an electrostatic nature, specific experimental and numerical examples are presented to provide inputs for an increased understanding of the underlying cause-and-effect relationships. Studying these systems can be seen as a matter of understanding how macroscopic scenarios arise from the cooperative behaviour of sub-parts or competing mechanisms (nonlinearities and interdependencies on various spatial and temporal scales). Through a critical assessment of the properties displayed by the resulting structures (which appear in the form of one-dimensional circuits formed by aligned particles, planar accumulation surfaces, three-dimensional compact structures resembling “quadrics”, micro-crystallites or fractal aggregates), we discuss a possible classification of the related particle attractors in the space of parameters according to the prevailing effect