I have a design which the background has been cut out and saved as transparent in a PNG file. What would be the best way to turn this into an SVG and retain it's transparency? When I save this as an SVG the transparent background is now solid white but I need the exact shape as it was cut without the background. Also I need this in SVG format to import into another application.

When I use the Import function, the png's alpha is usually active and nothing needs to be done other than convert to vector (if needed).

If the import does not work properly for you, perhaps you can upload the png?

Also, importing .png file into the Inkscape and saving it as .svg does not change the raster image into the vector image. To do so you`ll need to trace or convert it, and than saving it in .svg will make it a scalable vector graphic / svg.

p.s.
While in Inkscape, check Document properties for the background color/alpha settings.

Thank you for your responses guys. In respect to the import and convert to vector, does this mean I just need to change the document properties for the transparency, yes?

Also Maestral. You say I must either trace or convert it. What is the process of properly converting this to svg? Are the steps above enough? This will be useful for me to know because tracing some of these will be extremely difficult and I will also have to repeat this process for many pngs that I have.

Perhaps this would explain a difference among vector and raster images.

Simple import of raster image in Inkscape does not makes it a vector image, and therefore remaining the transparency of the background will not affect that fact.