There are several sustainable options for wrapping gifts. We don't have to tear up paper!
What I used here are pillow cases, shawls and scarfs. Silk ribbons (that I had saved over time) were used to tie the gifts, they are fun to open.
These gifts were for the family only. So, all the wrapping fabrics went back to their original purpose after the gifts were opened.
if the gifts are for others, the wrappings could be part of the gift. Example - Kitchen or hand towels, pillow cases for kids, blankets, table cloth, table runner, scarfs, shawls etc.