In this Account, we focused on a unique class of inclusion compounds, intermetallic clathrates, which exist in a variety of structures and exhibit diverse physical properties. These compounds combine covalent tetrahedral frameworks with rattling guest atoms situated inside their framework cages. Tetrels, the group 14 elements, are the basis for conventional clathrates because they fulfill the bonding requirement of four electrons per framework atom. In analogy to the replacement of Ge with GaAs in semiconductors, we focused on unconventional tetrel-free clathrates with frameworks composed of phosphorus and late transition metals. Compared to tetrels, these elements exhibit greater flexibility in their local coordinations and bonding. Tetrel elements cannot tolerate high deviations from regular tetrahedral coordinations. Thus, they exile a number of theoretically predicted framework topologies that are composed of a single type of polyhedral cage with square faces, such as the truncated octahedron. Unconventional clathrates are capable of stabilizing both envisaged and unique, unforeseen topologies. Clathrate structures with guest atoms held inside their cages by weak electrostatic interactions are predicted to be efficient thermoelectrics due to their low thermal conductivities. Unconventional clathrates may exhibit ultralow thermal conductivities, below 1 W m-1 K-1, without a need for heavy elements in their frameworks. The different chemical natures of transition metals and phosphorus led to their segregation over different framework positions, fulfilling the elements' specific local coordination and bonding requirements. This resulted in the formation of short- and long-range ordered superstructures with complex phonon dispersions and ultralow thermal conductivities. Aliovalent substitutions are commonly used to tune charge carrier concentrations in materials science. They are often performed under the "doping" assumption that substitutions with neighboring elements in the periodic system should not affect the parent structure but only adjust the charge carrier concentrations. This is not the case for unconventional clathrates. We investigated the tunability of the prototype Ba8Cu16P30 clathrate by the aliovalent substitution of Cu with either Zn or Ge. These substitutions resulted in significant alterations of the local chemical bonding and led to the rearrangement of the whole crystal structure. Remarkable thermoelectric properties were achieved for the substituted unconventional clathrates, exhibiting an overall order of magnitude increase in the thermoelectric performance. Aliovalent substitution allowed us to vary the charge carrier concentration in one structure type within the limits of the structure's stability. Exceeding these limits in the Ba-Cu-Zn-P system resulted in a transition from the covalent 2c-2e bonding found in conventional clathrates to the multicenter bonding common for metal-rich intermetallic compounds. This caused the complete rearrangement of the crystal structure into a new unique clathrate where a majority of the framework atoms are five- and six-coordinated, and all metal atoms are joined in Cu-Zn dumbbells. Our work shows that unconventional clathrates exhibit diverse crystal structures and unique chemical bonding, which result in tunable transport properties. While they are similar to their tetrel counterparts in some ways, they are very different in others. Specifically, the high thermal and chemical stabilities and low thermal conductivities of unconventional clathrates make them promising bases for further development of thermoelectric materials.