A general theory is presented to calculate the Rydberg and continuum states of an atom or molecule in external magnetic and parallel or crossed magnetic and electric fields of arbitrary strength. We show how the photoabsorbtion and photoionization spectra can be obtained for an atom or molecule at any excitation energy and we demonstrate how the complex resonance structure present in the classically chaotic energy region of the spectrum can be analyzed and understood. Results are presented for lithium in magnetic fields of 6.1 T and for hydrogen and rubidium in crossed magnetic and electric fields of intensity 6 T and 2975 Vcm, respectively. The theory combines quantum-defect theory, R-matrix propagation, and two and three-dimensional frame transformations. Much of the observed experimental resonance structure in the continuum can be understood in terms of complex perturbed Rydberg series.