"We now address two of the drawbacks [of the standard Big Bang theory]... the flatness problem and the horizon problem. In the early 1980's, Alan Guth resolved these two problems with his inflationary theory. His basic idea was that the universe enters a false vacuum state shortly after the Big Bang, then tunnels out and expands exponentially. We choose to discuss Guth's original model (now called classical model or old inflation) for pedagogic reasons. Guth's model has many nice qualitative features; it does not work quantitatively. Therefore, A. Linde, A. Albrecht, P. Steinhardt, and others constructed new models as remedies. It is not clear which of the new models is correct..."