This thesis studies the magnetism of the A'2A''A'''Mn4O12 columnar ordered quadruple perovskite manganites. The magnetic structures of five distinct members of this family of manganite perovskites has been determined using neutron scattering and magnetometry measurements. Point charge calculations of the crystal electric field, percolation calculations and a symmetry and group theoretical based approach to data analysis has been used to motivate the microscopic origins of the determined magnetic phases, and the physical mechanisms driving the observed magnetic phase transitions. Four regions of the magnetic phase diagram have been observed; a collinear ferrimagnetic phase, a Γ-point canted ferrimagnetic phase, a Z-point canted ferrimagnetic phase, and a magnetic phase characterised by well correlated collinear ferrimagnetic order punctuated by randomly dispersed clusters of antiferromagnetic order. We show that competing superexchange interactions and disorder can tune these manganites into different magnetically ordered phases. In these systems we observe two mechanisms for driving spin reorientation phase transitions. In Tm2MnMnMn4O12 the competition between rare-earth (Tm3+) and transition metal (Mn) anisotropies coupled via f-d exchange drives the spin reorientation, as is typical for distorted perovskites. In R2CuMnMn4O12 (R = Y or Dy) an alternative paradigm for spin reorientation was observed, which originated in frustrated Heisenberg exchange interactions, and the competition between Dzyaloshinskii- Moriya and single-ion anisotropies. Our studies on magnetic dilution in the Sm2MnMnMn4-xTixO12 systems have shown that they demonstrate an unusual variation in transition temperature, suggesting a departure from mean field physics. We observed a spin doped Griffiths phase in Y2MnMnMn4O12, and the coexistence of two magnetically distinct phases below Tc.