The site I am working on did not have their site submitted to Google Search Console (formerly Google Webmaster Tools). I submitted the site and a sitemap that auto updates. Google is crawling the site daily (about 30 pages a day). Under Search Traffic > Links to Your Site it shows no data is availible. I thought it was because it was a newly submitted site, but it has been two months now.
Moz seems to have the same issue. Moz does show inbound links, but their are some that we think should really help us that are not shown. For instance, the Dallas Morning News wrote this article. They have a high DA and PA. Also, iliveindallas.com has an article about us that is still on the front page. That was a few weeks ago but also does not show up on Moz or Google SC.
We are trying to be selective about the links we are getting. That they are follow links from reputable sites. Worried that both Google and Moz are not showing them.