The report contains a survey of past discoveries and current knowledge concerning the facial structure of convex polytopes, including some connections with linear programming. Details of proofs are considered unimportant instead, reliance is placed on statements of definitions and theorems and on references to the literature, along with an account of unsolved problems and a few historical remarks. The section headings are as follows 1. Four landmarks 2. Polytopal d-tuples 3. Poly topal graphs 4. Paths in polytopes 5. Additional results and problems. Bibliographic notes are included in each section. They refer to the list of more than a hundred publications which appears at the end of the paper.