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The hemispheric coupling phenomenon of solar activity cycle was discovered as early as the mid-20th century, and it is one of the most common topic in the long-term spatio-temporal evolution of the Sun, while the observational features and physical mechanism of hemispheric coupling have not been completely understood. The theoretical model of solar magnetohydrodynamics driven by this phenomenon is helpful in studying the basic information of the spatio-temporal evolution of solar activity cycle, and is also of great value to the short- and medium-term forecast of solar activity as well as the space weather. Here, we first give the discovery and observational history of the hemispheric coupling of solar activity. And then, the basic observational features of hemispheric coupling at different spatio-temporal scales and their possible mechanism are summarized. Finally, we give a discussion about the important unresolved issues and development trends in this important field.

The study on the 1.3–1.7 yr period of the solar and geomagnetic activities is very important for understanding the possible physical processes in the solar-terrestrial coupling system. The sunspot is the most prominent magnetic field structure in the solar photosphere, and the Ap index is an important indicator for the global geomagnetic activity level. The 1.3–1.7 yr period for the sunspot number and the geomagnetic Ap index is obtained by the synchro-squeezing wavelet transform, and the phase relationship between them is studied by the cross-correlation analysis. The main results are as follows: (1) The 1.3–1.7 yr period of the geomagnetic Ap index and sunspot number exhibits an intermittent evolutionary characteristics, and changes continuously with the time; (2) the geomagnetic Ap index has a higher periodic component in the odd solar cycles than the neighboring even solar cycles, which is characterized by fluctuations; (3) the phase relationship between the geomagnetic Ap index and the sunspot number is not always invariant, in most cases the geomagnetic Ap index lags behind the sunspot number, except in the 18th and 22th solar cycles.