To wipe out organised crime you need to arrest their mid-bosses and raid their locations.
Final mission for each crime faction is a story mission, unlocked by reducing the boss & location count of that faction.
To find out suspicious locations, assign your sergeants on patrol duty.
To find out owners of locations use patrols, informants or crime scene investigations.
Raiding a place needs evidence and known location owner. Successful raid makes the location neutral/civilian owned.
Police units have no upkeep and cost nothing to hire
Promotions will provide you with more sergeants, more units and more units to missions. They are earned via story steps.
Crime scenes are spawned after missions and after certain assignments. You can perform three assignments there, but crime scenes will be removed soon so make sure you assign units immediately.
Interrogate suspects requires evidence but will reduce boss-count.
Arresting units takes place from behind, or from knocked out state.
Arresting boss units will reduce their count in strategy layer, helping you wipe out the criminal faction.
Police brutality is bad. Shooting first, attacking civilians, killing unarmed or lightly armed crooks will lead to internal investigations.
Criminals will try to flee so make sure you arrest or stop them before they do that.