There are two categories of undergarments for hanfu: Zhong Yi/中衣 (middle clothes) and Nei Yi/内衣 (inner clothes). As you can guess, the hanfu that is worn as the outermost layer is called Wai Yi/外衣 (outer clothes).
1) Zhong Yi are worn by both males and females. Appearance-wise they look like regular hanfu, but they can only be worn inside of other clothes. They are usually white, but can be other colors as well. Going outside with only Zhong Yi on is regarded as impolite, but they can be worn as lounge-wear and/or pajamas at home. Zhong Yi is required when dressing in formal attire for important events.
For females (note - the top can be tucked into the skirt):
For males:
Here’s a photo of Zhong Yi:
2) Nei Yi commonly refers to the chest undergarments that women wear with hanfu. They play the same role as a brassiere does, but they are longer, covering the belly as well. Their appearance has changed throughout history, as can be seen in picture below:
For the sake of simplicity, I will just introduce the type of Nei Yi that is currently the most commonly worn with hanfu: Mo Xiong/抹胸. The Mo Xiong is the square/rectangular undergarment that is exposed when paired with parallel-collar ruqun (left - pink Mo Xiong) and beizi (right - blue Mo Xiong):
The Mo Xiong can come with or without straps. Here is how to wear the strapless version:
And here are some Mo Xiong with straps:
For further info/pics, I have an underwear tag you can take a look at.
