It is of the greatest importance that mathematics educators, together with those who set educational policies, prioritize the development of high ability, giftedness, and mathematical creativity. This issue of ZDM Mathematics Education presents ten evocative, in-depth research studies, most of them highly detailed, addressing a set of closelyrelated questions. The articles invite a broad, coherent response. The comments that follow are organized around four broad areas of key research questions pertaining to mathematical creativity and giftedness: • What do we mean by creativity and giftedness (or high ability) in mathematics? • What learning environments or activities foster mathematical creativity and high ability? • How should teacher education contribute to encouraging mathematically creative activity and nurturing giftedness? • How do educational policies foster or inhibit mathematical creativity and the development of high-ability students, and how do societal trends or forces contribute toward or impede these goals? In fact, I came to the task of responding to the articles in this volume having these areas of inquiry already in mind, as the most fundamental and/or most pressing in the field. Let us consider the studies in the current volume in relation to each of these in turn. Sections  ۲, ۳, and 4 elaborate on the first three areas of needed research, posing more specific questions and considering how the studies in the current volume address some of those questions. Discussions and findings are highlighted area by area, and comments are offered in response. Section ۵ addresses the fourth area, raising some points in connection with the value of prioritizing creativity and giftedness in mathematics education. This is a value I share with all of the present authors, but which is far from universally held. Section  ۶ offers some brief concluding remarks. Besides commenting on findings in the articles, I shall point to some important issues and themes that are not discussed. The reader should understand that this is not intended as criticism—no article or collection of articles can possibly take everything into account. Rather it is a way to map out the landscape of overarching topics requiring attention, and to situate the research presented in this special issue within that landscape.