Political philosophy asks what authority is, what makes it legitimate, what citizens owe one another, and what a good political order would look like. It is older than political science and broader than political theory: it asks not how politics works but how it should, and whether that distinction can be sustained.
The Western arc runs from Plato's question about the just city and Aristotle's classification of constitutions, through Augustine and Aquinas fusing the classical inheritance with Christian theology, to the social contract theorists of the seventeenth and eighteenth centuries. Hobbes, Locke and Rousseau recast political authority as something constructed by the governed instead of given by nature or God. The nineteenth century turned to liberty, class and the consequences of industry. The twentieth nearly abandoned the subject as unscientific, until Rawls's A Theory of Justice (1971) revived normative political philosophy almost single-handedly.
The field is divided about its own method, and the divisions are not minor. Analytic political philosophers treat historical texts as sources of arguments to be assessed on their merits. The Cambridge school of Skinner and Pocock insists that arguments be read as interventions in the specific disputes that produced them. Straussians read the canon for meanings deliberately concealed from hostile readers. These approaches produce different canons and opposite readings of the same books.
Most major Western philosophers contributed to political philosophy without making it their primary subject, which is why it overlaps so heavily with moral philosophy, jurisprudence and theology. Its persistent difficulty is that the central questions have not converged on answers in two and a half millennia. What justifies coercion, how liberty weighs against equality: there is genuine disagreement about whether the lack of settlement reflects the immaturity of the field or the nature of the questions.