  Investigations of three-body nuclear systems using pionless effective field
theory ($\mathrm{EFT}_{\not{\pi}}$) are reviewed. The history of
$\mathrm{EFT}_{\not{\pi}}$ in $nd$ and $pd$ scattering is briefly discussed and
emphasis put on the use of strict perturbative techniques. In addition
renormalization issues appearing in $pd$ scattering are also presented. Bound
state calculations are addressed and new perturbative techniques for describing
them are highlighted. Three-body breakup observables in $nd$ scattering are
also considered and the utility of $\mathrm{EFT}_{\not{\pi}}$ for addressing
them.
