Judaism has no hierarchy, no ordination that confers sacramental power, and no body able to bind the whole. What it has is halakha and the process by which halakha is decided, and Orthodox governance is that process.
A ruling begins with the texts: Talmud, then the great codes, Maimonides's Mishneh Torah and above all Joseph Karo's Shulchan Aruch of 1565, printed with the glosses of Moses Isserles that supply Ashkenazi practice where it differs from Sephardi. On top of those sits a vast literature of responsa, written answers by recognised authorities to specific questions, running continuously from the early middle ages to the present and now covering electricity, transplants, artificial insemination and internet use.
Authority attaches to the posek, the decisor, and it is conferred by nothing except recognition. A community follows a particular rabbi because it accepts him, and a scholar of exceptional standing may be followed far beyond his own community. Chief rabbinates exist, Israel has two, Ashkenazi and Sephardi, with statutory power over marriage, divorce, conversion and burial for Jews in Israel, but their authority outside Israel is nil, and large parts of Israeli Orthodoxy do not defer to them religiously even while operating under their legal jurisdiction.
Within Orthodoxy the main internal line is between Modern Orthodoxy, which holds full observance together with secular education, professional life and, in most of its forms, religious Zionism, and the Haredi world, which holds a deliberate separation. The institutional expressions of Modern Orthodoxy include Yeshiva University in New York and the religious-Zionist yeshiva network in Israel.
The live disputes are the role of women in ritual and leadership, on which the movement's right and left have effectively separated, and conversion standards, which have become a matter of Israeli state law as well as religious law.