The long lifetime and the evolving nature of industrial products make them subject to technical debt at different levels. Despite multiple years of research on technical debt management, our industrial experience shows that introducing systematic technical debt management in a large-scale company is very challenging. To identify the challenges, we provide a conceptual framework for holistic debt management across the product development value stream, which takes multiple categories of debt and their interplays into account. We use this framework to identify multiple challenges that are still open to be explored by the research community. Due to the practical nature of technical debt management, we believe this paper can guide the research community on the needs of industry for the effective application of technical debt management in practice.