The extended Fibonacci family continues to be a fertile ground for exploration, creativity, pattern recognition, and conjecturing. After a brief introduction to Fibonacci, Lucas, Pell, and Pell-Lucas polynomials, and the corresponding numbers, we will investigate if distinct Fibonacci(Lucas) square tiles can be used to tile F_(n+1) x F_n (L_(n+1) x L_n) floors. We will construct combinatorial models for these four polynomial families, and the corresponding numbers. If time permits, we will then study Fibonacci and Pell walks.