This paper intends to introduce the reader into Level Mixing Spectroscopy (LEMS), and to the results obtained with it so far. LEMS is a rather recent method used to study the quadrupole interaction of isomeric states in solid hosts, and was developed at Leuven. After an introduction dealing with both the theoretical background and the experimental set-up, a detailed comparison will be made with the Time Differential Perturbed Angular Distribution (TDPAD)-method. It turns out that LEMS is well suited for very high spin states in the ns-ms lifetime region. In the second part, the results in isotopes of Bismuth (10−-isomers in202-204-206Bi and the 21/2+-state in207Bi), Astatine (211At, 29/2+-and 39/2−-states;210At, 15−-and 19+-isomers;209At, 29/2+-isomer and208At, 16−-level) and Francium (213Fr, 29/2+-and 65/2−-levels;212Fr, 15−-and 27−-states and211Fr, 29/2+-and 45/2−-isomers) are discussed. The spin values range from 10 up to 65/2 and the lifetime region extends from 70 ns up to 13 ms, which proves already the applicability of LEMS. The results will also be compared to other data known so far in the208Pb-region.