Thinking about the strengthening of the police function, performance is an area scarcely explored in Latin America. At the core are effectiveness and legitimacy. Some studies focus on efficiency against crimes and criminals. None addresses the legitimacy and effects of police actions on citizen support. Nor are lessons and good practices known. There are lines of innovation that represent opportunities: neuroscience and information and communication technologies would help to capitalize on organizational knowledge and intelligence. In particular, criminal analysis helps a lot. Analysts can focus on the examination of social impacts and not only on criminal activity in a territory, thus enhancing strategic, operational and administrative analysis. Criminal mapping is useful in diagnostics, characterization of patterns of criminal activity, and operational targeting. But, it is only occasionally used to determine impacts, validate solutions and generate collective learning in local prevention. For the police to improve their performance, crime mapping should be oriented towards citizens in a territory and not just examining criminal activity in that place. The geography of insecurity is a necessary activity for community work and social cohesion, which are at the base of the legitimacy and effectiveness of the police.