The hypergrowth of technological scale-ups is receiving growing research attention from TIM (Technology and Innovation Management) scholars. While much is researched and written about hypergrowth's strategic topics, scaling of technology, and physical assets, less attention is given to the internal challenges faced by rapidly and massively scaling firms. In this paper, we argue that if TIM scholars focusing on product development and new market entrance are to advance knowledge concerned with hypergrowth of scale-ups, they need to join the conversation with the general management scholars who focus on how to manage people in a rapidly developing context. We build our arguments by drawing on Penrose's theory of firm growth, which emphasizes that growth is a function of management capacity and possession of resources, and which suggests that massive scaling in one type of resource will lead to imbalances of other types of resources. We also draw on the cognitive theory of the firm, which suggests that a firm's priorities are the outcome of its top managers' mental models. Consequently, we put forward that technology-based firms, successful in technology scaling, will create issues and challenges on the human side of organizations. These challenges include HR issues, like hiring and turnover, leadership challenges, and organizational culture, which are often the focus of management research. To inspire new research, we review research evidence from technology and management literature integrating available evidence concerned with the “growing pains” of hyperscaling firms. We identify at least three important drivers of hypergrowth in technology scale-ups that affect the firm's internal processes: i) time pressure, ii) constant change, and iii) scarcity of resources. These context drivers put the workforce in a stressful situation due to a) expanding job demands, b) massive hiring, c) changing leadership requirements, and d) evolving organizational culture. We integrate our findings into an organizing framework that dynamically relates hypergrowth to effects in organizations. We conclude this paper with suggestions for how the growing pains can be addressed by future research on hypergrowth firms.