Zeolitic　imidazolate　frameworks　(ZIFs)　are　an　important　subclass　of　metal-organic　frameworks　(MOFs).　Recently,　we　reported　a　new　kind　of　MOF,　namely　tetrahedral　imidazolate　frameworks　with　auxiliary　ligands　(TIF-Ax),　by　adding　linear　ligands　(Hint)　into　the　zinc-imidazolate　system.　Introducing　linear　ligands　into　the　M2+-imidazolate　system　overcomes　the　limitation　of　imidazole　derivatives.　Thanks　to　the　synergistic　effect　of　two　different　types　of　ligands,　a　series　of　new　TIF-Ax　with　interesting　topologies　and　a　special　pore　environment　has　been　reported,　and　they　have　attracted　extensive　attention　in　gas　adsorption,　separation,　catalysis,　heavy　metal　ion　capture,　and　so　on.　In　this　review,　we　give　a　comprehensive　overview　of　TIF-Ax,　including　their　synthesis　methods,　structural　diversity,　and　multi-field　applications.　Finally,　we　also　discuss　the　challenges　and　perspectives　of　the　rational　design　and　syntheses　of　new　TIF-Ax　from　the　aspects　of　their　composition,　solvent,　and　template.　This　review　provides　deep　insight　into　TIF-Ax　and　a　reference　for　scholars　with　backgrounds　of　porous　materials,　gas　separation,　and　catalysis.