Operations research and optimization in healthcare and disease modeling have received significant attention in the last three decades. This article surveys several perspectives of operations research techniques in kidney disease, such as graph theory, queueing theory, Markov chain, and phase-type distribution (PTD). The kidney-related problems include kidney exchange problem, the modeling of kidney disease progression, kidney transplantation, and the complex relationship between chronic kidney disease (gradual loss of kidney function over time) and acute kidney injury (sudden episode of kidney failure in a few hours or a few days). Each section is summarized by some discussion regarding the limitation of proposed methods in the literature. Finally, the article is concluded by offering some research direction to fill in the gaps in the literature.