Inkscape is a open source (GNU) vector drawing software with full SVG compliance, although it does not have all SVG features yet, like CSS and animation. It is very useful to convert a variety of vector formats to web use, with really good exporting of SVG and PNG, and importing PDF, Illustrator, Corel Draw and Microsoft Visio, among other.
The drawing tools are the high point of this app, been the tool of choice for icon makers and illustrators. There are several filter effects that are GPU accelerated to better performance. And its features can be extended using Python plugins.
Bottom line is, this the best drawing app for web graphics.
Inkscape interface is based in Corel Draw and Xara Designer, so if you come from Adobe software it will feel unfamiliar. But there are plenty of good tutorial online, and the free book "Inkscape: Guide to a Vector Drawing Program" by Tavmjong Bah.
Compared to Adobe Illustrator the printing features are really basic. Only in the last version it started supporting physical units, instead of just pixels. There is CMYK, color profiling, proofing, but nothing fancy.
Another low point of Inkscape is the update cycle. From 2010 to 2015 they only made bug fixes releases, with no new features added. But from 0.91 forward they are back on track.
If you just want to convert vector files I highly recommend Inkscape.
If you are just learning vector drawing, Inkscape is an accessible and powerful starting point. Maybe it is all you will ever need.
An Adobe Illustrator user may feel out of place. You will have to give it a chance to see if it have everything you need. Chances are it will worth it, but truth be told, Illustrator have much more features. If you use them all is another question.
We are creating and modifying graphics for web interfaces. Now we are able to share and edit assets with multiple developers and designer without additional software licenses.
We can also analyze SVG code in ways other vector editors do not enable.