New transition-metal-containing Zintl phases, Ca21Mn4Bi18 and Ca21Mn4Sb18, have been synthesized by high-temperature reactions, and their structures have been determined by single-crystal X-ray diffraction. Ca21Mn4Bi18 crystallizes in the monoclinic space group C2/c (No. 15, Z = 4) with a = 17.470(2) angstrom, b = 17.392(2) angstrom, c = 17.208(2) angstrom, beta = 93.253(2)degrees (R1 = 0.0405, wR2 = 0.0840) and is isostructural with the recently reported Ca21Mn4Sb18. The compound with the same formula, which is also reported herein, is in turn a new polymorph of Ca21Mn4Sb18 and crystallizes in the monoclinic space group C2/m (No. 12, Z = 4) with a = 17.415(6) angstrom, b = 16.567(6) angstrom, c = 17.047(6) angstrom, beta = 92.068(4)degrees (R1 = 0.0432, wR2 = 0.0788). This new polymorph of Ca21Mn4Sb18 is isostructural with another related compound, Sr21Mn4Sb18. Despite the similarity in their chemical formulas, the structures of Ca21Mn4Bi18 and Ca21Mn4Sb18 are very different: Ca21Mn4Bi18 contains unique [Mn4Bi10] cluster anions made up of four MnBi4 tetrahedra connected through edge-sharing. The structure of Ca21Mn4Sb18 features edge- and corner-shared MnSb4 tetrahedra, which make [Mn4Sb11] tetramers. The latter are linked to each other through external Sb-Sb bonds to form larger isolated [Mn8Sb22] polyanions. Electronic band structure calculations performed using the TB-LMTO-ASA method show a small band gap at the Fermi level, suggesting narrow-gap semiconducting behavior for both compounds.