1. The simple chemostat; 2. The general chemostat; 3. Competition on three trophic levels; 4. The chemostat with an inhibitor; 5. The simple gradostat; 6. The general gradostat; 7. The chemostat with periodic washout rate; 8. Variable yield models; 9. A size-structured competition model; 10. New directions; 11. Open questions; Appendix A. Matrices and their eigenvalues; Appendix B. Differential inequalities; Appendix C. Monotone systems; Appendix D. Persistence; Appendix E. Some techniques in nonlinear analysis; Appendix F. A convergence theorem.