We study the Local Group (LG) dwarf galaxy population using cosmological simulations of volumes selected to resemble the surroundings of the Milky Way (MW) and Andromeda (M31) galaxies. The simulations, from the APOSTLE project, indicate that the total mass within 3 Mpc of the pair's midpoint (M 3Mpc ) typically exceeds ∼ 3 times the sum of the virial masses of the two primaries and that the dwarf galaxy formation efficiency per unit mass is uniform throughout the volume. This suggests that MW and M31 satellites should make up fewer than one third of all LG dwarfs within 3 Mpc. This is consistent with the fraction (28 per cent) of galaxies with stellar mass M * > 10 7 M that are satellites. In addition, the total number of such galaxies (42) suggests, for the APOSTLE galaxy mass-halo mass relation, a total LG mass of M 3Mpc ∼ 10 13 M . At lower galaxy masses, however, the satellite fraction is substantially higher (42 per cent for M * > 10 5 M , or 42 out of 99). If this is due to incompleteness in the field sample, then ∼ 50 dwarf galaxies at least as massive as the Draco dwarf spheroidal are missing from our current LG field dwarf inventory. The incompleteness interpretation is supported by the pronounced flattening of the LG luminosity function below M * ∼ 10 7 M , and by the scarcity of low-surface brightness LG field galaxies: whereas ∼ 40 per cent of all M * > 10 5 M MW/M31 satellites have effective surface brightness below Σ eff = 26.5 m V /arcsec 2 , only 1 out of all field dwarfs does. The simulations indicate that most missing dwarfs should lie near the virial boundaries of the two LG primaries, and predict a trove of nearby dwarfs that await discovery by upcoming wide-field imaging surveys.