For illustrations, .svg is smaller, more scalable, and much clearer, and has no background. If you use a .png for an illustration, it is more pixelated when putting it online. We recommend to all of our clients to use .svg online as much as possible, especially for logos. 

.svg is created from the original file used to create the illustration. Typically, Adobe Illustrator or Adobe InDesign - .ai or .eps file.

We recommend that clients ensure they get the source files in their hands for all graphics they outsource to designers. If they won't give you the .ai or .eps, don't hire them. It's really hard to search around and find it later, and may not even be available. Then, if you want to make changes or improve quality by converting things to .svg, you have to recreate the logo and pay again. 

Converting a .png to a .svg doesn't work well. 

When to use various file types:

• .svg - illustrations in all cases, except email marketing. Email clients don't accept .svg files, use a .png in that case
• .png - illustrations for email marketing
• .jpg - photos
• .ai or .eps or .psd - source files, get them for all the content created for you!
  • .psd is a photoshop file that has multiple layers.