The Constitution both protects the free exercise of religion and bars government establishment of it. Those commitments can pull in opposite directions, and most contemporary disputes involve where accommodation ends and privileging begins.
Free exercise doctrine has shifted over time between requiring the government to justify burdens on religious practice and holding that neutral laws of general applicability need no special justification. Federal and state religious freedom statutes were enacted partly in response to those shifts.
Establishment questions cover public funding flowing to religious institutions, religious expression in public schools, and displays on government property. Recent decisions have generally been more permissive of religious participation in public programs than earlier doctrine was.
Accommodation questions arise across many contexts: employment scheduling, health care conscience protections, prison and military practice, land use for houses of worship, and vaccination requirements.