Molecular braids represent one of the most fascinating topological networks in the fields of supramolecular chemistry and crystal engineering. In this Tutorial Review we provide an overview of the sustainable exploration of those metal-organic frameworks (MOFs) with the topology of molecular braid. Since the first example of the triple-stranded molecular braid in MOFs was reported by our group in 2005, another five attractive molecular braids in MOFs have already been prepared through several different pathways by us and other groups. Indeed, these known examples include the triple-, quintuple- and sextuple-stranded molecular braids. Besides the molecular braids found in MOFs, this type of unique topological network was also observed in organic co-crystals, and the only example of this is discussed in context as well.