Twitter made some massive changes in their site and application, also how the whole Twitter Card things work. Now the whitelisting is easier then ever.
Twitter Card is now all over in Twitter App & Mobile Web
From the screenshot you could see now in Twitter Apps Twitter shows card in home page and everywhere by default. People reported it looks more like the way Facebook embed link. But here difference is its all about Card. So, if you have Summary Card it will show Image with little text, for Gallery & Product it shows accordingly.
No more Waiting for Twitter Whitelisting
Now you dont have to wait for Whitelisting. Install Twitter Cards Meta plugin, configure, follow the steps, if your link validates you will be automatically approved for more basic Card type. But special Card type like Player Card & App Card are little complex, and always needs special verification.
No more custom Background in Twitter Desktop site
Twitter silently removed your custom background from their desktop design (in mobile there was no custom bg anyway). Specially you will notice when you visit your profile page. No solid color, no custom image, its all same for any profile you visit. Though you will see your custom Background in home page and others, not just on profile, now all profile page is very same in basic look. You could read more about this new at TNW.
How its good thing for you?
To be short and stay in this points
1) You dont have to wait and worry about getting whitelisted for common Card type. If you visit Twitter Community Forum you will understand how many people has issue with it.
2) In Mobile site using Card will get lots of benefit, first and foremost your Tweet looks more compelling with Card enabled, its more then just a link share, it has a glimpse of story behind, your CRT is going to jump, your impression is going to increase.
3) Some people see it negatively as Twitter removed the background in profile pages, I am kind of optimistic. If you look at Facebook, they hardly offer any option to customize profile. And in this way, now everybody has a fair play ground. Tricky marketer wont be about to exploit it. You don't have to worry about whose Profile looks better. You are still able to change Profile image, cover image, you just have one less thing to worry about.
So, day by day its being imminent that Twitter Card is important. So, make sure you have Twitter Cards Meta installed, and followed all best practice. After all its the only plugin that lets you have different Twitter Card in different post, and works automatically, means you don't have to configure anything manually per post.