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The large set problem in the combinatorial design theory has a long history and important applications. The related research work had been quite slow in making progress for a long period of time due to its sophistication. Being benefited and motivated by some new methodology the research in the large set problem has taken on a promising posture in recent thirty years. In this paper, we give a comprehensive summary about the development of large sets and overlarge sets for some types of classical triple systems. In addition, we obtain new results that there exist an ${\rm OLKTS}(2\cdot13^n+1)$ and an ${\rm OLRMTS}(3\cdot5^n)$, where $n\geq0$.