There have been many attempts to understand the emotions. In particular there has been a strong thrust towards what has been termed "affective computing", where human emotion is monitored by a computer, or emotional responses to human activity are attempted to be incorporated in a computer system, an avatar or a robot. But in order to achieve "affective computing" it is necessary to know what is being computed. That is, in order to compute with what would pass for human emotions, it is necessary to have a computational basis for the emotions themselves. What does it mean quantitatively if a human is sad or angry? How is this affective state computed in their brain? How are emotions "felt" in the consciousness system? It is these questions, on the very core of the computational nature of the human emotions, which is addressed in this chapter. A proposal will be made as to this computational basis based on the well established approach to emotions as arising from an appraisal of a given situation or event by a specific human being. Finally how emotions can become conscious will be discussed at the end of the chapter.