Simultaneousspeech translation (SimulST) is the task in which output generation has to be performed on partial, incremental speech input. In recent years, SimulST has become popular due to the spread of multilingual application scenarios, like international live conferences and streaming lectures, in which on-the-fly speech translation can facilitate users' access to audio-visual content. In this paper, we analyze the characteristics of the SimulST systems developed so far, discussing their strengths and weaknesses. We then concentrate on the evaluation framework required to properly assess systems' effectiveness. To this end, we raise the need for a broader performance analysis, also including the user experience standpoint. We argue that SimulST systems, indeed, should be evaluated not only in terms of quality/latency measures, but also via task-oriented metrics accounting, for instance, for the visualization strategy adopted. In light of this, we highlight which are the goals achieved by the community and what is still missing.