  We search for novel two-dimensional materials that can be easily exfoliated
from their parent compounds. Starting from 108423 unique, experimentally known
three-dimensional compounds we identify a subset of 5619 that appear layered
according to robust geometric and bonding criteria. High-throughput
calculations using van-der-Waals density-functional theory, validated against
experimental structural data and calculated random-phase-approximation binding
energies, allow to identify 1825 compounds that are either easily or
potentially exfoliable, including all that are commonly exfoliated
experimentally. In particular, the subset of 1036 easily exfoliable
cases---layered materials held together mostly by dispersion interactions and
with binding energies up to $30-35$ meV$\cdot\text{\AA}^{-2}$---provides a
wealth of novel structural prototypes and simple ternary compounds, and a large
portfolio to search materials for optimal properties. For the 258 compounds
with up to 6 atoms per primitive cell we comprehensively explore vibrational,
electronic, magnetic, and topological properties, identifying in particular 56
ferromagnetic and antiferromagnetic systems, including half-metals and
half-semiconductors.
