Many markets have seen a shift from the idea of buying and moved to leasing instead.Arguably, the latter has been a major catalyst for their success. In the wake of this shift,we study in this thesis leasing concepts from an algorithmic perspective. In particular,we design theoretic models, study their inherent diculty, and devise provably good(often optimal), ecient algorithms, with the goal to cope with real-world resourceleasing scenarios.A major diculty faced by most of these markets is the uncertainty of future demands.Consider a subcontractor who leases expensive resources from other companies to rentthem out to clients. The subcontractor may buy long/expensive leases for some resource,just to realize later on that no more requests are issued for this resource in subsequenttime steps. Or, the subcontractor may buy short leases, just to notice later on thathaving bought a longer lease would have cost less.In attempt to capture this diculty, our algorithms tend to be online, thus providingsolutions in the present without knowing the future.