This paper is a survey article on the polyhedral realizations of the crystals \(B(\infty)\) and \(B(\lambda)\) for a dominant integral weight \(\lambda\) (see [Y. Kanakubo and T. Nakashima, Commun. Algebra 48, No. 11, 4732–4766 (2020; Zbl 1484.17023); J. Algebra 574, 327–374 (2021; Zbl 1484.17024)]). The polyhedral realization is one of well-known combinatorial realizations of crystals. This realization was introduces as the images of the crystal embedding \(\Psi_\iota: B(\infty) \rightarrow \mathbb{Z}_\iota^\infty\) and \(\Psi_\iota^\lambda: B(\lambda) \rightarrow \mathbb{Z}_\iota^\infty[\lambda]\), where \(\iota\) is a infinite sequence of indices with a certain condition. In the paper, the authors explain how \(\operatorname{Im}(\Psi_\iota)\) and \(\operatorname{Im}(\Psi_\iota^\lambda)\) are described inside the infinite \(\mathbb{Z}\)-lattice in terms of linear inequalities. The authors then explain the tableaux descriptions for the polyhedral realizations. Several explicit examples are explained in the paper.