The realization of Kitaevs honeycomb magnetic model in real materials has become one of the most pursued topics in condensed matter physics and materials science. If found, it is expected to host exotic quantum phases of matter and offers potential realizations of fault$-$tolerant quantum computations. Over the past years, much effort was made on 4d$-$ or 5d$-$ heavy transition metal compounds because of their intrinsic strong spin$-$orbit coupling. But more recently, there have been growing shreds of evidence that the Kitaev model could also be realized in 3d$-$transition metal systems with much weaker spin$-$orbit coupling. This review intends to serve as a guide to this fast$-$developing field focusing on systems with d$^7$ transition metal occupation. It overviews the current theoretical and experimental progress on realizing the Kitaev model in those systems. We examine the recent experimental observations of candidate materials with Co$^{2+}$ ions: e.g., CoPS$_3$, Na$_3$Co$_2$SbO$_6$, and Na$_2$Co$_2$TeO$_6$, followed by a brief review of theoretical backgrounds. We conclude this article by comparing experimental observations with density functional theory (DFT) calculations. We stress the importance of inter$-t_{2g}$ hopping channels and Hunds coupling in the realization of Kitaev interactions in Co$-$based compounds, which has been overlooked in previous studies. This review suggests future directions in the search for Kitaev physics in 3d cobalt compounds and beyond.
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