I wouldn't say there's a single trump card. Flamethrowers are good for clearing rooms, and making the soldier less vulnerable as well as being more general-purpose, grenades are even better. Assault weapons, specifically fully automatic machine guns, give individual soldiers the sort of weight of fire that's critical in close quarters. On a personal level, modern urban warfare also utilizes satchel weapons, anti-tank guns, or purpose-built anti-tank/assault guns intended for bunker busting purposes to "mouse-hole"; rather than going through predictable doors, windows, or stairs, instead soldiers can punch holes in the walls, floors, and ceiling. If you had to say there's a single trump card, it'd definitely be the soldiers themselves. Training in urban warfare is key to knowing how to use all these fancy tools, and willingness to fight goes without question. That, however, is a bit of a cop-out on my part; well-trained and motivated soldiers are a significant force multiplier in any sort of battle, rather than just urban warfare.
Your best case study for modern warfare, especially if you're considering an asymmetric situation, could include Israel's occasional forays into Gaza or Second Fallujah. More equivalent forces could be found in the Red Army's conduct of the Battle of Stalingrad. For a fairly modern counter-example, the Siege of Sarajevo or much of Syria are probably good case studies for how not to fight a protracted urban battle. The two Battles of Grozny twist both ways. The first battle in 1994 and the First Chechen War was completely destructive to the Russian Army in spite of the eventual capture of the burned-out husk of the city; foolish tactics, particularly the use of unsupported armoured spearheads in an urban environment (Especially in the '90s..."What do you call a tank in a city? A target.") and a converging attack along multiple unsupported axes led to defeat in detail in the initial blow, and lack of a coherent strategy was crippling. The second attempt in 1999 and the Second Chechen War was much more effective, though I won't say it compares to the IDF (whatever you may think of their politics, few do, after all); the vulnerable tanks were held back, and the assault to be conducted by trained infantry under artillery and FAB support. On the flip side, the rebels in Grozny had turned the city into a fortress by setting mines in roads, building bunkers near apartments, digging trenches everywhere and utilizing the sewers to permit protected mobility between buildings (compare to the tunnels of Gaza proper), and establishing a coherent and solid plan for withdrawal and redeployment. The result of these preparations on both sides was actually a bit of a mug's game either way; the time to take the city wasn't significantly shortened and the end result (Russian victory) was the same, but the casualties on the Russian side were drastically improved and the actual long-term strategic result was very different.