Primary and secondary education in Texas is handled at the public level by school districts, of which there are over 1,000 and (with one exception, a district operated by the City of Stafford, a suburb of Houston) which are independent of any city or county authority.
Although a district may contain the name of the primary city (such as the Dallas Independent School District), the districts do not necessarily align with city or county boundaries. As an example, the City of Dallas is served not only by its namesake district, but also by eight additional districts located primarily in other cities. Concurrently, the Dallas school district also serves students in all or parts of 17 other cities. Two districts (Boles and Boys Ranch) have geographic areas concurrent with nonprofit facilities for orphaned or troubled students.
The Texas Education Agency (TEA) has limited oversight of school districts; however, it has the authority to close a district if it repeatedly fails to properly educate students (a notable example was in 2005 when the Wilmer-Hutchins district -- a district with even worse performance than any of the big city districts -- was finally closed after allegations of teachers helping students cheat on state exams). TEA is organized into 20 regions, which exist solely to provide assistance to districts; the regions have no authority over districts.
In addition to public schools, Texas has many charter and private schools. TEA has limited jurisdiction over charter schools (mainly there is a very strict cap on the number of charter schools which can operate, and the cap is statewide as opposed to regional). TEA has absolutely no jurisdiction over private schools, which vary widely in size. The majority of private schools have some level of affiliation with a church or religious order, and while some schools have sought accreditation (mainly to induce parents who may be concerned over whether their child's transcript will be accepted into university) others strictly oppose doing so due to a general distrust over such groups which they claim are "liberal" and "hostile to Christianity".
TEA also has no jurisdiction over homeschooling. Though Texas was previously a difficult state for homeschooling, in recent years it has become one of the most friendly states, due in large part to the state court case Leeper v. Arlington ISD which clarified the lack of governmental jurisdiction over the practice.
Unlike many states where public and private schools are governed by one agency for athletic and similar contests, there are several agencies covering these contests. The primary agency is the University Interscholastic League (UIL, as its name suggests it is operated by the University of Texas), which governs all public schools as well as some charter and two all-male private schools (Dallas Jesuit and Houston Strake Jesuit, which due to their size would overwhelm the other private schools). The Texas Association of Private and Parochial Schools (TAPPS) governs most of the larger private schools (especially those associated with Christian churches or groups), while the Southwest Preparatory Conference -- which also has one member in neighboring Oklahoma -- governs many non-sectarian private schools. There are also several smaller groups which govern much smaller private schools. As a result, unlike in most states where the predominant athletic programs are private schools, most of the predominant athletic programs in Texas are public schools.