Research problems are crucial in the sense that they provide new research with purpose and justification. So why, despite the abundance of guidance available from an extensive methods literature, do graduate students often struggle to develop compelling research problems? This article argues that the process of developing research problems epitomises the insecurity of doing research. We focus in particular on the anxiety that graduate students often seek to avoid or alleviate through a range of counterproductive coping strategies. The existing literature on research problems focuses predominantly on the technical aspects of doing research while neglecting how anxiety might affect the research process. This article seeks to rectify this shortcoming by providing advice on how graduate students can face such anxiety, and how professors can assist them in this endeavour. Drawing on theories about identity and anxiety, the article explains the allure of coping strategies such as gap-filling, while arguing that anxiety is not necessarily a negative emotion to be avoided at all costs, but integral to learning and creativity. It concludes by suggesting that compelling research problems can be constructed through the formulation of narratives that try to embrace anxiety, instead of seeking premature resolutions.