Typically, coarse-graining methods can be divided into two categories: top-down and bottom-up approaches. In the top-down approach such as Martini, relatively simple functional forms with a fixed number of ajustable parameters are selected for parameterization of CG models to match the experimentally measured macroscropic properties. However, it is uncertain whether the top-down CG models can accurately reflect the underlying microscopic physics due to its lack of a rigorous CG mapping from atomic degrees of freedom. rameterized with atomistically detailed information. The bottom-up CG method attempts to capture the molecular details and reproduce the microscopic behaviors of the mapped atomistic model. There are several promising algorithms to develop systematic bottom-up coarse-grained models, including multiscale coarse-graining (matching effective force residuals), relative entropy (matching information loss), and Iterative Boltzmann inversion and Inverse Monte-Carlo (matching structural properties). Although bottom-up approaches hold promise in the development of faithful CG models, there are still several significant challenges that remain unresolved. The first pertains to the transferability of the CG models across varying environments such as (thermodynamic) state points and compositions. Another challenge revolves around ensuring the consistency and accurate representation including structural, dynamical, and thermodynamical properties. Numerous efforts have been dedicated to improving bottom-up CG modeling. The problem of transferability within such models often arises due to inadequate training data to parameterize the selected CG model. To address this limitation, for instance, one viable strategy involves the utilization of the "extended ensemble" variational principle. This method attempts to determine a set of transferable potentials that optimally describe CG interactions for multiple systems across multiple state points under the multiscale coarsegraining framework. A similar idea that leverages information from multiple state points was also developed in the IBI method. A single set of potential functions, i.e., a force field, that provides an optimal compromise for modeling a range of systems and thermodynamic state points. More recent advances in improving the transferability of coarse-grained models include the dual-potential method by Noid et al., ultra-coarse-graining with semi-global density potentials by Jin, Yu, and Voth, microcononical relative entropy by Pretti and Shell, and a recent extension of IBI by Qian and co-workers. Aside from the transferability issue, the representability of CG models in comparison to their corresponding AA models remains a persisting concern. One of the most common examples is the trade-off between accurately reproducing pairwise correlations and a dramatic overestimation of pressure. This issue is evident in methodologies like the IBI approach. To mitigate the pressure overestimation predicament, the IBI method employs a technique involving linear rescaling within pairwise interactions. This rescaling is iteratively refined to align with the desired pressure target. However, a drawback of this approach is that, while it aims to improve pressure prediction, it cannot explicitly guarantee concurrent matching of key structural attributes, such as radial distribution functions (RDFs). Consequently, this approach could potentially lead to a reduction in the accuracy of structural predictions.