Applying evolutionary methods to the generation of music and art is a relatively new field of enquiry. While there have been some important developments, it might be argued that to date, successful results in this domain have been limited. Much of the present research can be characterized as finding adhoc methods that can produce subjectively interesting results. In this paper, it is argued that a stronger overall research plan is needed if the field is to develop in the longer term and attract more researchers. Five ‘open problems’ are defined and explained as broad principle areas of investigation for evolutionary music and art. Each problem is explained and the impetus and background for it is described in the context of creative evolutionary systems.