Wolf (Canis lupus) depredations of livestock are a ubiquitous source of conflict in every country where wolves and livestock overlap. We studied the spatial and temporal variation of wolf depredations of livestock in Montana during 2005–2015, including evaluations of targeted control efforts and public harvest as potential means to reduce depredations. During this time we collected spatial data for all confirmed wolf-livestock depredations, tallied the annual number of depredation events within hunting districts, and collected data for variables potentially predictive of depredation events. We decomposed variation in depredation data into 2 distinct components: the binary presence or absence of depredation events in each district-year, and the count of depredation events in district-years with ≥1 event. We found that presence-absence of depredations increased with wolf presence and wolf density, increased with livestock density, were highest at intermediate proportionate areas of agricultural land, and were a recurrent phenomenon such that districts with depredations the previous year were more likely to continue having them. Targeted removal, but not public harvest, significantly reduced the recurrent presence of depredations. The number of conflicts in district-years with ≥1 depredation event was positively correlated with wolf density, cattle density, intermediate proportionate areas of forested land, and the number of events during the previous year. Public harvest reduced the counts of depredation events in areas where conflict reoccurred, though with a modest predicted effect size of 0.22 fewer depredations/district-year, or 5.7 fewer depredation events statewide/year (8% of the annual average). Minimizing livestock losses is a top priority for wolf management. These results shed light on the broad-scale patterns behind chronic problems and the effectiveness of wolf management practices in addressing them.