Block copolymers (BCPs) remain a central topic in soft matter science, driven by their ability to self-assemble into periodic nanostructures with tunable symmetries and domain sizes. This self-assembly often proceeds with additional structuring of BCP domains, such as crystallization [1,2] and mirror-symmetry breaking [3]. Representative examples of BCPs applications include nanolithography [4], membranes [5], energy materials [6] and drug delivery vehicles [7]. The rational design of such materials requires detailed understanding of how molecular features control self-assembly under various thermodynamic and kinetic conditions. This challenge spans multiple length and time scales, motivating a combined push from advanced experiments and theory [8-11].

On the theory front, self-consistent field theory (SCFT) remains a powerful tool for predicting equilibrium morphologies and is continually being extended to handle increasingly complex polymer architectures, fluctuation effects [12], chiral chains [13], semi-flexible polymers [14], and BCP blends [15]. These methods have recently been accelerated using machine learning [16] and gradient-based solvers [17], and combined SCFT- coarse-grained molecular dynamics approach [18] allowing exploration of high-dimensional parameter spaces.

To go beyond mean-field approximations, field-theoretic simulations (FTS) that explicitly incorporate composition fluctuations have been developed with highly efficient algorithms [19], enabling more accurate predictions [20] and providing a powerful connection to experiments [8], capturing the rich, phase behaviour of BCPs.

On the other hand, mesoscopic simulation techniques—including, dissipative particle dynamics (DPD) [21,22], hybrid strategies [23-25] combining field- and particle-based representations, and phase-field methods—have advanced rapidly. These methods capture kinetic pathways in nonequilibrium processes and now enable efficient access to long time and length scales while preserving the essential physics of polymers [26].

Experimentally, BCP systems are studied using techniques such as cryo-transmission electron microscopy (cryo-TEM) [27], synchrotron scattering [28], and scanning probe microscopy [29,30] to probe their nanostructural order, defects, and phase transitions. Advances in polymer synthesis now enable the creation BCPs of variety of architectures including sequence-defined multiblock BCPs [31]. Confinement, external fields, and templated substrates have been leveraged to direct self-assembly of BCPs [4,32-34].  Recent experimental efforts also target the design of hierarchical [35] and chiral morphologies [36], expanding the structural complexity accessible via BCPs [37].

A clear recent trend is the convergence of theory and experiment toward addressing materials-by-design problems in increasingly complex BCP systems [8,9,38].