Buoyant jets have been a topic of interest due to their presence in various natural and industrial phenomena, as well as in our daily lives. Covering extensive literature, our focus in this review article is on free, miscible buoyant jets with small-density differences (under the Boussinesq approximation) within uniform and stagnant environments. We examine the latest research on Newtonian jet flows and expand our scope to their viscoplastic counterparts, reflecting a burgeoning trend in contemporary literature. Our analysis covers negatively buoyant, pure, and positively buoyant jets, via delving into their dynamics. This includes regime classifications and key jet characteristics, such as laminar length, penetration length, mixing behavior, velocity profiles, and turbulence parameters. In particular, the effects of the key governing dimensionless parameters, including the Reynolds number, the Froude number, the Bingham number, the viscosity ratio, and the injection angle, on these characteristics are explored.