Affective computing has proven to be a viable field of research comprised of a large number of multidisciplinary researchers resulting in work that is widely published. The majority of this work consists of computational models of emotion recognition, computational modeling of causal factors of emotion and emotion expression through rendered and robotic faces. A smaller part is concerned with modeling the effects of emotion, formal modeling of cognitive appraisal theory and models of emergent emotions. Part of the motivation for affective computing as a field is to better understand emotional processes through computational modeling. One of the four major topics in affective computing is computers that have emotions (the others are recognizing, expressing and understanding emotions). A critical and neglected aspect of having emotions is the experience of emotion (Barrett, Mesquita, Ochsner, and Gross, 2007): what does the content of an emotional episode look like, how does this content change over time and when do we call the episode emotional. Few modeling efforts have these topics as primary focus. The launch of a journal on synthetic emotions should motivate research initiatives in this direction, and this research should have a measurable impact on emotion research in psychology. I show that a good way to do so is to investigate the psychological core of what an emotion is: an experience. I present ideas on how the experience of emotion could be modeled and provide evidence that several computational models of emotion are already addressing the issue.