Despite a longstanding and widespread influence of the diagnostic approach to mental ill health, there is an emerging and growing consensus that such psychiatric nosologies may no longer be fit for purpose in research and clinical practice. In their place, there is gathering support for a "transdiagnostic" approach that cuts across traditional diagnostic boundaries or, more radically, sets them aside altogether, to provide novel insights into how we might understand mental health difficulties. Removing the distinctions between proposed psychiatric taxa at the level of classification opens up new ways of classifying mental health problems, suggests alternative conceptualizations of the processes implicated in mental health, and provides a platform for novel ways of thinking about onset, maintenance, and clinical treatment and recovery from experiences of disabling mental distress. In this Introduction to a Special Section on Transdiagnostic Approaches to Psychopathology, we provide a narrative review of the transdiagnostic literature in order to situate the Special Section articles in context. We begin with a brief history of the diagnostic approach and outline several challenges it currently faces that arguably limit its applicability in current mental health science and practice. We then review several recent transdiagnostic approaches to classification, biopsychosocial processes, and clinical interventions, highlighting promising novel developments. Finally, we present some key challenges facing transdiagnostic science and make suggestions for a way forward. What is the public health significance of this article? Traditional diagnostic systems may no longer be fit for purpose for classifying mental ill health, facilitating understanding of its core underlying biopsychosocial processes, nor driving clinical developments. Here we propose that 'transdiagnostic' approaches have the potential to better represent the clinical and scientific reality of mental health problems, reflecting the complexity, dimensionality and comorbidity that is the norm in clinical practice.