A systematic study of the structural and magnetic properties of three-dimensionally frustrated lanthanide garnets Ln3A2X3O12, 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 Gd3+ spins; no magnetic ordering is observed for T ≥ 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 molGd-1) is observed for Gd3Sc2Ga3O12 at 2 K, in a field of 9 T. The performance of Dy3Ga5O12 as a magnetocaloric material surpasses the other garnets with Ln = Tb, Dy, Ho.