The present invention provides heterodimer pairs that can comprise a first heterodimer and a second heterodimer wherein each heterodimer comprises an immunoglobulin heavy chain or fragment thereof and an immunoglobulin light chain or fragment thereof. At least one of the heterodimers can comprise one or more amino acid modifications in the CH1 and/or CL domains, one or more amino acid modifications in the VH and/or VL domains, or a combination thereof. The modified amino acid(s) can be part of the interface between the light chain and heavy chain and are typically modified to create preferential pairing between each heavy chain and a desired light chain such that when the two heavy chains and two light chains of the heterodimer pair are co-expressed in a cell, the heavy chain of the first heterodimer preferentially pairs with one of the light chains rather than the other. Likewise, the heavy chain of the second heterodimer typically preferentially pairs with the second light chain rather than first.