This thesis is concerned with the measurement and interpretation of isotope shifts. The first part describes an experimental determination of isotope shifts in the 4s^{2 1}S<subo</sub> - 4s5s¹ S_o transition of neutral calcium. This measurement was performed using the method of Doppler-free two-photon absorption spectroscopy in an atomic beam of the natural mixture of calcium isotopes. The laser was stabilized and scanned by means of an external, pressure-swept etalon, and its scan was calibrated by recording the transmission fringes of the laser through a confocal etalon, 2m in length. This calibration etalon was stabilized with reference to an I₂-stabilized Helium- Neon laser. The isotope shifts of all the stable isotopes of calcium were measured; the results are believed to be free from systematic error and so the standard deviations are derived from the scatter of the results. A Isotope Shift ^δv^A-44/MHz 40 -1169.99(28) 42 -563.66(7) 43 -263.67(6) 46 534.34(70) 48 1023.50(7) These results are compared with other accurate measurements of isotope shifts in calcium by laser spectroscopy, by means of the King plot. All the measurements are consistent except for the only odd isotope ⁴³Ca, which, in this transition, unlike those in the other experiments, is free from hyperfine structure. The best values of the isotope shifts are thus determined by a least squares procedure. The mass and field shifts are separated using the values of δ<r²> determined from muonic isotope shifts, and this leads to more accurate values of δ<r²>. The second part of the thesis concerns the interpretation of anomalous isotope shifts in samarium. Pairs of spectral lines had been found for which the shifts of even-even isotopes did not lie on a straight line on a King plot. These deviations are interpreted as evidence for the insufficiency of first-order perturbation theory for the treatment of isotope shifts in a number of levels of the samarium spectrum. By comparing shifts in transitions connecting these levels with shifts in transitions connecting levels for which first-order perturbation theory appears to be a good approximation, values of off-diagonal matrix elements are found. These are not required to be unreasonably large to explain the observed deviations.