The paper is concerned with the history of the spherically symmetric static problem solution of General Relativity found in 1916 by K. Schwarzschild [1] [2] which is interpreted in modern physics as the background of the objects referred to as Black Holes. First, the modern interpretation this solution which does not exactly coincide with original solution obtained by K. Schwarzschild is discussed. Second, the basic equations of the original Schwarzschild solution are presented in modern notations allowing us to compare existing and original solutions. Finally, a modification of the Schwarzschild approach is proposed allowing us to arrive at the exact solution of the Schwarzschild problem.