There’s a ladder with a method of computing the exchange term. Each higher level adds an extra ingredient to the mix, which (hopefully) increases accuracy. Higher accuracy comes at higher computational cost, so the lower levels are more computationally efficient.
From simple to accurate:
LDA: uses density n
GGA: add gradient of density
meta-GGA: adds kinetic energy density
hybrid SIC: treats exchange exactly
RPA-like: adds unoccupied orbitals and their energies