Asymptotic integration has turned out to be a powerful method to determine the deficiency indices and spectra of higher order differential operators. Since the general method is by now well established we shall only outline this method and illustrate typical results and properties via examples. In addition to the calculation of deficiency indices, the location and multiplicity of the absolutely continuous spectrumwill be found as well as showing the absence of singular continuous spectrum. Finite singular pointswill also be considered. For unbounded coefficients new results arise from competing terms of the operators.