Within living cells, chromosome shapes undergo a striking morphological transition, from loose and uncondensed fibers during interphase to compacted and cylindrical structures during mitosis. ATP driven loop extrusion performed by a specialized protein complex, condensin, has recently emerged as a key driver of this transition. However, while this mechanism can successfully recapitulate the compaction of chromatids during the early stages of mitosis, it cannot capture structures observed after prophase. Here we hypothesize that a condensin bridging activity plays an additional important role, and review evidence - obtained largely through molecular dynamics simulations - that, in combination with loop extrusion, it can generate compact metaphase cylinders. Additionally, the resulting model qualitatively explains the unusual elastic properties of mitotic chromosomes observed in micromanipulation experiments and provides insights into the role of condensins in the formation of abnormal chromosome structures associated with common fragile sites.