In this survey paper we focus on aspects of the quality of teaching mathematics from several perspectives. We differentiate between effective aspects that are empirically proven and more normative ones that constitute "good teaching" but that are highly dependent on context. High quality of mathematics teaching includes characteristics from a generic point of view as well as those that rely upon more subject- and topic-specific features. In the paper we draw upon examples of the research traditions in Germany and in the US--where the discussion regarding quality of mathematics teaching has been particularly intensive--to provide a short overview about empirical key findings. We then describe open questions in this research field and conclude by proposing a conceptualization of high quality mathematics teaching that foregrounds the relationship between generic and topic-specific and also considers different possibilities for the measurement of the quality.