Cell theory states that:

1. All living organisms are composed of one or more cells. This means that cells are the fundamental building blocks of life.

2. The cell is the basic unit of structure and function in living organisms. This means that all the activities necessary for life occur within cells.

3. All cells arise from pre-existing cells. This means that cells don't spontaneously appear, but rather originate from other cells through cell division.

Therefore, the cell itself is the structural unit that underlies all living organisms, according to cell theory.