The bright Ca ii H2v and K2v grains, which are intermittently present in the interiors of network cells in quiet-Sun areas, should provide important diagnostics of the dynamical interaction between the quiet photosphere and the chromosphere above it, but their nature has so far eluded identification. We review the extensive observational literature on these grains and on related phenomena. We resolve various contradictions, connect hitherto unconnected observations, distill new constraints and relate signatures in the measurement domain to signatures in the Fourier domain. We then review interpretations and simulation efforts, adding computations of our own to illustrate modeling options. We conclude that the grains are a hydrodynamical phenomenon in which magnetic fields do not play a major role. The grains are due to interference between a pervasive standing oscillation with about a 180 s periodicity and an 8 Mm horizontal wavelength in the chromosphere and the wave trains of the evanescent p-mode interference pattern in the upper photosphere. The roles of short-period waves, shock formation and granular piston excitation and the issue of long-lived patterning remain open; we suggest avenues for further research.