Puffed up sleeves are short and gathered in a way to make them look like puffs.

They are a combination of cap sleeves and puffed sleeves.

Off-the-shoulder sleeves are not alien to us and have been in vogue for a while now.

the old Bishop-style dresses and shirts

Kimono sleeves are inspired by the Japanese traditional Kimono attire. 

Raglan sleeves come in all lengths and are a popular choice for bodycon dresses, casual tops, and T-shirts.