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At the LHC, the process of a Higgs boson decaying into bottom or charm quarks produced in association with a pair of top quarks, <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="normal">t</mi><mover accent="true"><mi mathvariant="normal">t</mi><mo>¯</mo></mover><mi mathvariant="normal">H</mi></mrow></semantics></math></inline-formula>, allows for an empirical exploration of the heavy-flavor quark Yukawa couplings to the Higgs boson. Accordingly, the cross-sections for the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="normal">t</mi><mover accent="true"><mi mathvariant="normal">t</mi><mo>¯</mo></mover></mrow></semantics></math></inline-formula> + heavy-flavor production without the appearance of the Higgs boson have been measured at the LHC in various phase spaces using data samples collected in pp collisions at <inline-formula><math display="inline"><semantics><msqrt><mi>s</mi></msqrt></semantics></math></inline-formula> = 7, 8 and 13 TeV with the ATLAS and CMS experiments. Flavor ratios of cross-sections of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="normal">t</mi><mover accent="true"><mi mathvariant="normal">t</mi><mo>¯</mo></mover></mrow></semantics></math></inline-formula> + heavy-flavors to <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="normal">t</mi><mover accent="true"><mi mathvariant="normal">t</mi><mo>¯</mo></mover></mrow></semantics></math></inline-formula> + additional jets processes are also measured. In this paper, the measured cross-sections and ratios are reviewed and the prospects with more data are presented.