A survey of effective characterizations of tree logics. If L is a logic, then an effective characterization for L is an algorithm, which inputs a tree automaton and replies if the recognized language can be defined by a formula in L. The logics L considered include path testable languages, frontier testable languages, fragments of Core XPath, and fragments of monadic second-order logic. Categories and Subject Descriptors F.4.1 [Mathematical logic and formal languages]: Mathematical logic; H.2.3 [Database management]: Languages-Query languages General Terms Languages, Theory