Nucleus is essentially composed of protons and neutrons, which are commonly known as nucleons. Interestingly, some of nucleons may group together and exhibit collective behavior inside a nucleus. Such clustering effects have been known since the early stages of nuclear physics because of the observation and description of α-cluster decay from many heavy nuclei. Subsequent studies demonstrated that cluster structures exist in many nuclear systems, especially in weakly bound or excited states, and are complementary to the shell-like structures. In this review article, we provide a brief historical recall of the field, and follow it with a conceptual and logical description of the major theoretical models that have been frequently applied in the literature to describe nuclear clustering. Experimental methods and progress are outlined, recent outcomes are emphasized, and perspectives relevant to future studies of heavy neutron-rich systems are discussed.