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For anyone familiar with magic.gov.uk (a UK government web-based GIS) I can shortcut this question by saying that I'm looking for the equivalent of the identify tool. For others, this is a tool which produces a report identifying the value of all the properties of any polygon from all selected layers on a click of the mouse.
So, say I had three layers, one with counties (name, population, area), one with nature reserves (name, area, type of reserve) and one with habitat (type, rarity, conservation status). I would like to be able to click on a point on the map (or draw a polygon), and produce a report which would list all the features from all the layers under that point, together with their attributes.
I'm using QGIS 2.18, but soon 3.