Below

Below means lower in position, rank, etc.; not as high as. This would be the opposite of above.

The farm is below the castle.

This morning the temperature was five degrees below zero. It usually stays above zero until after Christmas

She broke her leg just below the knee.

Under means lower in a vertical position, rank, etc.; covered by; controlled by. This would be the opposite of over.

The trash can is in the cupboard under the sink.

In her new position she has 15 people under her and four people over her.

I found my keys under the newspaper.