Of all current psychologies, psychoanalysis is the most engaged with the complex and chaotic dimensions of human development and suffering – intricate psychic processes, fluxing mental and physical states, unexpected shifts between clarity and confusion, big changes following small inputs, uncertainty about causes and locations – including whose thoughts belong to whom, and more. These crucial elements, however, have not always been taken up explicitly. Nonlinear dynamic systems theory (NLDS) provides an aesthetically pleasing and scientifically current framework for these factors and illuminates established clinical practice and theory. Through clinical examples, conceptual elaboration, and an account of the author’s growing interest in this field, this paper offers a user-friendly invitation to NLDS.