Imported PNG shows black instead of transparency in the background Importing a 'smoke' image as a plane shows no transparency.
Still have black background.



What other settings should I tweak?
The image you uploaded contains no alpha channel.



You can check the alpha channel for the image using the channel display switches at the bottom of the UV/Image editor window



Blender will not magically create an alpha channel for you, if the image contains none.



A half-ass solution (without getting into editing in an image editing app, or sourcing an image with a proper alpha channel), is to use the black and white representation of the image itself as a mask to control the mix between an emission and a transparent shader, so that the white pixels of the image will be emissive and the black ones transparent.