Solar activity is asymmetric in the two hemispheres in almost all cycles. This asymmetry is observed both in cycle amplitude and period. We have used about 90 years of sunspot-area data from the Kodaikanal Solar Observatory to study the north–south asymmetry in sunspot activity. The monthly mean sunspot-area showed the northern hemisphere dominated in Solar Cycles 16, 19, and 20, and the southern hemisphere dominated in Solar Cycles 18, 22, and 23. The 13-month smoothed data indicated that in Solar Cycle 17 and 21, the northern and southern hemisphere showed equal amplitude. Cumulative sunspot area showed that the northern hemisphere dominated in Solar Cycles 18, 19, 20, and 21, with a large difference between the two hemispheres in Solar Cycles 19 and 20. The northern hemisphere activity led by 12, 15, and 2 months in Solar Cycles 20, 21, and 22, respectively. No significant phase difference is found between the two hemispheres in Solar Cycles 16, 17, 18, 19, and 23. The wavelet technique is used to find Rieger-type periodicities in the sunspot cycles. The cross-wavelet analysis of these data sets showed several statistically significant common periodicities like the Rieger-type periodicities and quasi-biennial oscillations. The Gnevyshev gap was found in both the hemispheric data in Solar Cycles 16, 18, 21, 22, and 23. These results are consistent with the earlier reported characteristics of north–south asymmetry in sunspot-area data. These results suggest that the Kodaikanal Observatory data complement the existing sunspot data from other observatories to study solar activity over long and short periods.