The cell theory is an explanation of what cells are and why they exist.  The three main parts are:  1) All living things are made of cells and their products,  2) New cells are created by old cells dividing into two, and  3) Cells are the basic building units of life.  In 1665, Robert Hooke observed, with the aid of a crude compound microsope, the structure of a thin slice of cork.  The structure resembled stacks of hat boxes, or holding cells, so he called what he observed "cells".  In 1674, Anton von Leeuenhoek observed, in a sample of pond water, small animal-like creatures swimming around.  He probably was looking at Spyrogira, but he called these small organisms "animal-cules".  Theodore Schwann and Matthias Schleiden are responsible for formulating the first two parts of the cell theory, which was a scientific explanation of what these scientists had observed up to this point.  A few years later, Rudolph Virchow added the third part of the cell theory, that all things are composed of these basic building blocks called cells.

The cell theory was arrived at after much study of living cells due to the intellectual contributions of Matthias Schleiden who noted all plants contains cells, and in 1838 added that different parts of plants were composed of cells.  Theodor Schwann noted all living things contained cells and cell products and Rudolph Virchow, who noted that cells come from pre-existing cells. He pusblished his work in 1858 which rejected the idea of spontaneous generation, which was believed at the time. The cell theory states that 1. cells are the unit of structure of all living things 2. cells are the unit of function of living things--they carry out life processes 3. all cells come from pre--existing cells. These three scientists are credited with arriving at the cell theory. However, one cannot discount other contributers--the famous Francesco Redi experiment that proved maggots didn't come from rotten meat, but from adult lies laying eggs and the vast and detailed drawings by Anton Leeuwenhoek, who saw the cells of various living things using his early microscopes.