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While +3 dominates lanthanoid chemistry, certain elements show anomalous +2 or +4 states driven by the special stability of f^0, f^7, and f^14 configurations.

Ce^4+ (4f^0): Empty 4f subshell. Strong oxidising agent (E degree = +1.61 V). CeO2 used in catalytic converters and glass polishing. The only common +4 lanthanoid.

Eu^2+ (4f^7): Half-filled 4f gives extra exchange energy. Reducing agent. Similar ionic radius to Ba^2+, so EuSO4 is insoluble like BaSO4. Used for Eu separation.

Yb^2+ (4f^14): Fully filled 4f. Less commonly encountered than Ce^4+ or Eu^2+.

Tb^4+ (4f^7): Another route to half-filled stability, but rare.

Gd^3+ (4f^7): Already achieves half-filled stability in the standard +3 state, so no anomalous oxidation states. Has 7 unpaired electrons and maximum paramagnetism, used in MRI contrast agents.

Actinoids show wider OS ranges (+3 to +7) because 5f, 6d, and 7s energies are comparable. U can be +3 to +6 (UF6 for enrichment). The actinoid contraction is greater than lanthanoid contraction due to even poorer 5f shielding. All actinoids are radioactive.