  A systematic study of the structural and magnetic properties of
three-dimensionally frustrated lanthanide garnets $Ln_3A_2X_3\text{O}_{12}$,
$Ln$ = Gd, Tb, Dy, Ho, $A$ = Ga, Sc, In, Te, $X$ = Ga, Al, Li is presented.
Garnets with $Ln$ = Gd show magnetic behaviour consistent with isotropic
Gd$^{3+}$ spins; no magnetic ordering is observed for T $\geq$ 0.4 K. Magnetic
ordering features are seen for garnets with $Ln$ = Tb, Dy, Ho in the
temperature range 0.4 < T < 2.5 K, however the nature of the magnetic ordering
varies for the different $Ln$ as well as for different combinations of $A$ and
$X$. The changes in magnetic behaviour can be explained by tuning of the
magnetic interactions and changes in the single-ion anisotropy. The change in
magnetic entropy is evaluated from isothermal magnetisation measurements to
characterise the magnetocaloric effect in these materials. Among the Gd
garnets, the maximum change in magnetic entropy per mole (15.45 J K$^{-1}$
mol$_{\text{Gd}}^{-1}$) is observed for Gd$_3$Sc$_2$Ga$_3$O$_{12}$ at 2 K, in a
field of 9 T. The performance of Dy$_3$Ga$_5$O$_{12}$ as a magnetocaloric
material surpasses the other garnets with $Ln$ = Tb, Dy, Ho.
