The structure of light hypernuclei with strangeness and is investigated with the microscopic cluster model and the Gaussian expansion method (GEM). We emphasize that the cluster picture as well as the mean-field picture is invaluable to understand the structure of hypernuclei, hypernuclei and double hypernuclei. A variety of aspects of hypernuclei is demonstrated through a systematic study of -shell hypernuclei (,, , , , , ) and -shell ones (, ): for example, the appearance of genuine hypernuclear states with new spatial symmetry which cannot be seen in ordinary nuclei, the glue-like role of the particle which shrinks the size of nuclear core and thus reduces the (E2) value, and the halo and skin structures in and etc. The typical light hypernucleus is thoroughly investigated, including its production, structure and decay. Precise three-body and four-body calculations of , and using GEM provide important information on the spin structure of the underlying interaction, by comparing with recent experimental data from -ray hypernuclear spectroscopy. The coupling effect is studied in and . The binding mechanism of is discussed together with the possible existence of , emphasizing the fact that the study of is useful for extracting information on the interaction differing from that from . A systematic study of double- hypernuclei, constrained by the NAGARA data () within a four-body cluster model indicates that the recently observed Demachi–Yanagi event can be interpreted as the state of . The effect of hyperon mixing in and is investigated using one-boson-exchange potentials and quark-cluster-model interactions for the sector. A close relation between nuclear deep hole states and hypernuclei is discussed, emphasizing the selection rule for fragmentation of the -hole in light nuclei, which is promising for understanding the production mechanism of double- and twin- hypernuclei via -atomic capture.