Although governments intervene extensively across an ever-increasing range of activities, there are some problems that they are loath to address. These issues vary in size, scale and complexity. Some are local; others are national. A number are international or global. The impediments to action also differ. They may be technical, institutional or political. In some cases, there is no agreement even that a problem exists. In a few, by contrast, expert consensus on diagnosis and prescription may have been long-standing, even if yet to issue in concrete measures. What these issues share, however, is that their successful resolution would bring significant benefits to society, but that for whatever reason governments consider them too problematic to tackle. Hence they are consigned to the ‘too difficult box’. Where this happens the system of democracy is itself likely to be weakened. This article discusses these issues and introduces contemporary instances.