I have gone into Composer and specified the page background to be transparent. It still comes out white. Is there a solution?
First make the page background transparent in the sidebar under Composition - Page Settings - Page Background
Then for each map or item go to Item properties - Background and turn that off.
if you are trying to do this in QGIS 3.0, right click on the layout whitespace and select Page Properties. The setting to change the background is at the bottom of this dialog box.
Then you can export to a file format that supports transparency, i.e. PNG, via Composer - Export as image