Giant mineral dust particles (>75 mm in diameter) found far from their source have long puzzled scientists. These wind-blown particles affect the atmosphere’s radiation balance, clouds, and the ocean carbon cycle but are generally ignored in models. Here, we report new observations of individual giant Saharan dust particles of up to 450 mm in diameter sampled in air over the Atlantic Ocean at 2400 and 3500 km from the west African coast. Past research points to fast horizontal transport, turbulence, uplift in convective systems, and electrical levitation of particles as possible explanations for this fascinating phenomenon. We present a critical assessment of these mechanisms and propose several lines of research we deem promising to further advance our understanding and modeling.