Swarm intelligence (SI) is an emerging field of biologically-inspired artificial intelligence based on the behavioral models of social insects such as ants, bees, wasps, termites etc. Swarm intelligence is the discipline that deals with natural and artificial systems composed of many individuals that coordinate using decentralized control and self-organization. Most SI algorithms have been developed to address stationary optimization problems and hence, they can converge on the (near-) optimum solution efficiently. However, many real-world problems have a dynamic environment that changes over time. In the last two decades, there has been a growing interest of addressing Dynamic Optimization Problems using SI algorithms due to their adaptation capabilities. This paper presents a broad review on two SI algorithms: 1) Firefly Algorithm (FA) 2) Flower Pollination Algorithm (FPA). FA is inspired from bioluminescence characteristic of fireflies. FPA is inspired from the the pollination behavior of flowering plants. This article aims to give a detailed analysis of different variants of FA and FPA developed by parameter adaptations, modification, hybridization as on date. This paper also addresses the applications of these algorithms in various fields. In addition, literatures found that most of the cases that used FA and FPA technique have outperformed compare to other metaheuristic algorithms.