Partially adapted/copied from an earlier answer of mine:

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For much of the world until modern times there was no independent (ostensibly) and investigative group of institutions that sought to enact, enforce, and execute the law. Modern mediea translates modern Municipal police departments into institution such as the "town guard" (think the Skyrim Hold guards), but is that how it worked in the actual Middle Ages? In short, no.

For example in Anglo-Saxon England vigilantism, not a town guard or much less police force, was more or less the "default" of conflict resolution between equal members of society. There was no real distinction between vigilante justice and "official" justice, nor did independent courts, lawyers, etc... exist. Especially in the Early Anglo-Saxon period our ideas of objective justice and an independent judiciary/police force just simply were not a part of society. Justice and revenge were extremely interlinked, and the line between official prosecution and a lord taking justice "into his own hands" was significantly blurrier than we might imagine. Much scholarly ink has been spilled on the role of kings and their royal law codes in attempting to crack down on the feuds and disputes of their subjects. There has been a long standing assumption int he field that the Anglo-Saxon kings were moving in the direction of centralization of power and an increasing monopoly on the prosecution of wrong doers, taking power out of the hands of rival lords who would rather their disputes be settled among themselves. While this view is somewhat teleological, it is somewhat true in the broad strokes.

For certain crimes this was not necessarily the trend. Catching thieves in the act of theft, or chasing them down, was a devolved power, and very little "official" input was required for executing thieves, especially repeat offenders, from the time of England's unification onward. Other transgressions were different. There were numerous restrictions and exceptions and possible outcomes for murder for example. There could be any number of mitigating circumstances that would lessen the fine/penalty/penance paid for the crime such as whether the person murdered had harmed their murderer's relatives. But all of these permutations were still far removed from a centralized approach that royal figures might have wanted to implement.

Many scholars argue that the early Anglo-Saxon law codes were essentially efforts by the kings to preempt the cycles of feud and revenge that would result from transgressions by insisting on a royal presence in the paying of weregild, the amount of payment due to a slighted party. Many law codes provide for the involvement of royally appointed figures in the legal process, but this is misleading. Although royal law codes make provisions for reeves and sheriffs, we should not associate these figures with out later understandings of law enforcement. These figures were not necessarily a proto-police force as the name sherriff might imply, but instead royally appointed figures, or people acting under the auspices of royal authority, but in practice there seems to have been little effort at ensuring their objectivity. indeed Lambert posits that often in the case of a lord or other prominent figure that had committed a crime, the only person in the area who would be capable of putting together a force capable of executing justice on them was another lord, not the king's representatives. Later on in the Anglo-Saxon period, other practices such as banishment, ordeals, penance, and executions would come to play an increasing role in the prosecution of wrongdoing. But none of these ever really rose to the level of a police force, indeed Thomas Lambert points out that often times it was the aggrieved party acting on the orders of the royal figures (or claiming to), making this a system of legitimized vigilantism. Lambert concludes that over time the Anglo-Saxon kings were able to supersede the rights claimed by feud prone lords, but this was a long and involved process that was only somewhat complete by the time of the Norman conquest.