Resource allocation aims at allocating scarce resources to strategic agents in an efficient and fair manner. Due to its wide applications in real-life, finding such allocations satisfying specific properties is important for both theoretical research and industrial applications. In our work, we study three objectives: efficiency, fairness, and incentive, when allocating both divisible resource and indivisible resource. First, we consider the fair division of a heterogeneous divisible resource, which is well known as the cake cutting problem. We focus on designing truthful and envy-free mechanisms with the presence of strategic agents. Most results established by previous works in this setting all rely crucially on the free disposal assumption, meaning that the mechanism can throw away part of the resource at no cost. We study cake cutting mechanism design in two cases: without the free disposal assumption or with the free disposal assumption. Next, we study indivisible resource allocation. We consider three fairness notations with indivisible resources: maximin share guarantee, envy-free up to one good, and envy-free up to the least good. We study whether a mechanism exists when we combine these fairness notations with the connected piece assumption, Pareto optimality, and other moderate conditions. Last, we study a specific application, which we call the online roommate allocation problem. We show a polynomial-time online algorithm that achieves constant competitive ratio for social welfare maximization and both positive and negative results on the existence of an allocation satisfying different stability conditions in this online setting. Doctor of Philosophy