In this dissertation we study the Hamiltonicity and the uniform-Hamiltonicity of subset graphs, subspace graphs, and their associated bipartite graphs. In 1995 paper "The Subset-Subspace Analogy," Kung states the subspace version of a conjecture. The study of this problem led to a more general class of graphs. Inspired by Clark and Ismail's work in the 1996 paper "Binomial and Q-Binomial Coefficient Inequalities Related to the Hamiltonicity of the Kneser Graphs and their Q-Analogues," we defined subset graphs, subspace graphs, and their associated bipartite graphs. The main emphasis of this dissertation is to describe those graphs and study their Hamiltonicity. The results on subset graphs are presented in Chapter 3, on subset bipartite graphs in Chapter 4, and on subspace graphs and subspace bipartite graphs in Chapter 5. We conclude the dissertation by suggesting some generalizations of our results concerning the panciclicity of the graphs.