  Defects determine many important properties and applications of materials,
ranging from doping in semiconductors, to conductivity in mixed
ionic-electronic conductors used in batteries, to active sites in catalysts.
The theoretical description of defect formation in crystals has evolved
substantially over the past century. Advances in supercomputing hardware, and
the integration of new computational techniques such as machine learning,
provide an opportunity to model longer length and time-scales than previously
possible. In this Tutorial Review, we cover the description of free energies
for defect formation at finite temperatures, including configurational
(structural, electronic, spin) and vibrational terms. We discuss challenges in
accounting for metastable defect configurations, progress such as machine
learning force fields and thermodynamic integration to directly access entropic
contributions, and bottlenecks in going beyond the dilute limit of defect
formation. Such developments are necessary to support a new era of accurate
defect predictions in computational materials chemistry.
