Chromosome bi-orientation at the metaphase spindle is essential for precise segregation of the genetic material. The process is error-prone, and error-correction mechanisms exist to switch misaligned chromosomes to the correct, bi-oriented configuration. Here, we analyze several possible dynamical scenarios to explore how cells might achieve correct bi-orientation in an efficient and robust manner. We first illustrate that tension-mediated feedback between the sister kinetochores can give rise to a bistable switch, which allows robust distinction between a loose attachment with low tension and a strong attachment with high tension. However, this mechanism has difficulties in explaining how bi-orientation is initiated starting from unattached kinetochores. We propose four possible mechanisms to overcome this problem (exploiting molecular noise; allowing an efficient attachment of kinetochores already in the absence of tension; a trial-and-error oscillation; and a stochastic bistable switch), and assess their impact on the bi-orientation process. Based on our results and supported by experimental data, we put forward a trial-and-error oscillation and a stochastic bistable switch as two elegant mechanisms with the potential to promote bi-orientation both efficiently and robustly.