Short answers, pulled from the story.
Plato defines justice as a state of balance and harmony within the soul and the state where reason controls spirit and desire. He argues that a just person aligns internal conflicting aspects so that reason guides the spirited and desiring parts of the self. This internal order mirrors the ideal city where each class performs its proper function without overstepping.
The Judeo-Christian-Islamic tradition views justice as a governing concept derived directly from God and describes God as having righteousness and justice as the foundation of His throne. The divine command theory asserts that morality and justice are authoritative commands of God meaning murder is wrong because God says it is so. This perspective was challenged early on by Plato in his dialogue Euthyphro which posed the famous dilemma regarding the source of moral goodness.
Natural law posits that inherent laws derived from nature and universal moral principles are discoverable through reason while legal positivism emphasizes that laws are rules created by human authorities and are not necessarily connected to moral principles. Thomas Aquinas argued that human beings possess reason which is a spark of the divine and all human lives are sacred and of infinite value. John Locke stressed natural law's role in justifying property rights and the right to revolution independent of enacted laws.
Utilitarian justice fights crime through three primary mechanisms: deterrence which uses the credible threat of punishment to lead people to make choices that maximize welfare; rehabilitation which aims to change bad people into better ones by reducing the likelihood of causing unwanted things; and security which involves incapacitating irredeemable causers of bad things to protect society. Mill argued that our belief in the overwhelming importance of justice derives from the desire to retaliate against those who hurt us and the ability to put ourselves imaginatively in another's place known as sympathy.
John Rawls argues that each person is to have an equal right to the most extensive total system of equal basic liberties compatible with a similar system of liberty for all. He also states that social and economic inequalities are to be arranged so that they are both to the greatest benefit of the least advantaged and attached to offices and positions open to all under conditions of fair equality of opportunity. These principles are chosen behind a veil of ignorance that denies knowledge of personalities social statuses moral characters wealth talents and life plans.
Modern research indicates that the sense of justice is deeply rooted in human biology and psychology suggesting that reactions to fairness are wired into the brain. Studies at UCLA in 2008 showed that fairness activates the same part of the brain that responds to food in rats while research conducted in 2003 at Emory University involving capuchin monkeys demonstrated that other cooperative animals also possess such a sense. Victims of crime find respectful treatment information and having a voice important for a sense of justice as well as the perception of a fair procedure.