In a dividing eukaryotic cell, proper chromosome segregation requires the dynamic yet persistent attachment of kinetochores to spindle microtubules. In the budding yeast Saccharomyces cerevisiae, this function is especially crucial because each kinetochore is attached to a single microtubule; consequently, loss of attachment could lead to unrecoverable chromosome loss. The highly specialized heterodecameric Dam1 protein complex achieves this coupling by assembling into a microtubule-encircling ring that glides near the end of the dynamic microtubule to mediate chromosome motion. In recent years, we have learned a great deal about the structural properties of the Dam1 heterodecamer, its mechanism of self-assembly into rings, and its tethering to the kinetochore by the elongated Ndc80 complex. The most remarkable progress has resulted from defining the fine structures of helical bundles within Dam1 heterodecamer. In this review, we critically analyze structural observations collected by diverse approaches with the goal of obtaining a unified view of Dam1 ring architecture. A considerable consistency between different studies supports a coherent model of the circular core of the Dam1 ring. However, there are persistent uncertainties about the composition of ring protrusions and flexible extensions, as well as their roles in mediating ring core assembly and interactions with the Ndc80 complex and microtubule.