I wanted to make some 3D infographics, so I imported some vector images into blender via Inkscape. Normally, I can edit and move the points on a curve through all three dimensions, but for some reason these will only move on the x and y axes. I want to make the arrows point up and around as well, but this kinda impedes it.
Using a 2D curve implies that the Local Z coordinate of each control point is 0.
From the Blender manual's page about the topic:
By default, new curves are set to be 3D, which means that Control Points can be placed anywhere in 3D space. Curves can also be set to 2D which constrain the Control Points to the Curve’s local XY axis.
In a 2D curve you can't even set it's origin's Z coordinate with the 3D cursor. It is forced to lay on the plane where the the control points are.
You should switch the curve nature to 3D to be able to move them up and down.