Suicide prevention is a major health care responsibility in need of new perspectives. This study reviews Zero Suicide, an emerging approach to suicide prevention that embraces the aspirational goal of zero suicides among patients treated in health care systems or organizations. Zero Suicide is gaining international momentum while at the same time evoking objections and concerns. Fundamental to Zero Suicide is a multilevel system view on suicide prevention, with three core elements: a direct approach to suicidal behaviors; continual improvement of the quality and safety of care processes; and an organizational commitment to the aspirational goal of zero suicides. The rationale and evidence for these components are clarified and discussed against the backdrop of concerns and objections that focus on possible undesired consequences of the pursuit of zero suicide, in particular for clinicians and for those who are bereaved by suicide. It is concluded that it is rational to pursue zero suicides as an aspirational goal, provided the journey toward zero suicides is undertaken in a systemic and sustained manner, in a way that professionals feel supported, empowered, and protected against blame and inappropriate guilt.