Jacutingaite, Pt${}_2$HgSe${}_3$, has emerged as a model van der Waals material linking mineralogy, solid-state chemistry, and topological quantum physics. Single crystals of bulk Pt${}_2$HgSe${}_3$ was experimentally synthesized under high-pressure and high resolution angle-resolved photoemission spectroscopy had revealed a gapped Dirac nodal-line structure along with the surface states with multiple saddle points and van Hove singularities. Furthermore, under hydrostatic pressure, transport measurements shows a structure phase transition accompanied by superconductivity, with $T_c$ reaching approximately to 4.4~K at 88.8~GPa. Density functional theory calculations predict bulk Pt${}_2$HgSe${}_3$ to possesses dual topology, characterized by weak $Z_2$ topology and mirror-symmetry-protected crystalline topology. Monolayer Pt${}_2$HgSe${}_3$ was predicted to realize a Kane–Mele-type quantum spin Hall state with a spin–orbit induced gap of $$0.15–0.5eV,aresultsupportedbyearlyexperimentalsignatures.Othertheoreticalstudiespredictthattheelectronicstructureandtopologicalpropertiescanbetunedbylayerthickness,strain,electricfields,andpressures.Bilayersareshowntobeinitiallytrivialduetolayer-internalinversionasymmetry,butwithencapsulationwithinhexagonalboronnitrideundergoeselectronicallydriventopologicalphasetransitionwhichnarrowsthetrivialbandgap,andamodestout-of-planeelectricfieldre-invertsthebandstorestoretheirtopology,thoughthesemechanismsremaintobeverifiedexperimentally.Thisresearchupdateconsolidatesthetheoreticalandexperimentaladvancesacrossbulk,monolayer,andbilayerforms,withaparticularfocusonchemicaldoping,heterostructureengineering,andpressure-inducedsuperconductivity,thelastofwhichhasbeenexperimentallyobservedinbulkPt$_2$HgSe$_3$. Benchmark values such as band gaps, valley splittings, and critical temperatures are summarized to provide a reference for ongoing studies. We evaluate the prospects of jacutingaite based materials for realizing quantum spin Hall, quantum anomalous Hall, and topological superconducting states with the major challenges associated with their synthesis, structural stability, and device integration. This study brings together the experimentally established properties and theoretically predicted tunability and highlights strategic directions for advancing jacutingaite-based systems toward practical applications in spintronics, valleytronics, and emerging quantum technologies.