Particle-laden flows of sedimenting small heavy solid particles or droplets in a carrier gas have strong inter-phase coupling even at low volume fractions. The slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The analysis of inertial aerosols in homogeneous shear reveals three fundamental mechanisms contributing to the formation of clusters: (1) the preferential concentration of inertial particles in the stretching regions of the flow (2) particle-trajectory crossing (PTC) and (3) a Rayleigh-Taylor instability due to the vertical stacking of particle-rich and particle-depleted regions. Simulations are conducted in Euler-Lagrange and Euler-Euler formalisms. The Euler-Lagrange simulation method, based on particle tracking, capture all three effects but suffer from lack of scalability. Euler-Euler methods, based on a kinetic description, offer better scalability but require extreme care in the presence of PTC.