## 1 Introduction  
Porous materials have always attracted high scientific interest because of their outstanding performance and potential applications in various fields, such as gas adsorption and separation [1; 2], energy storage [3], air and water purification processes [4; 5; 6], drug delivery [7; 8; 9], molecular separation [10; 11], catalysis [12; 13], sensing [14], optoelectronics [15], and preparation of superhydrophobic surfaces [16]. Several properties of the bulk materials depend on their porosity, and huge opportunities are offered today by the possibility of tailoring different porous structures. In particular, porous materials display extremely high specific surface area (SSA) and outstanding adsorption properties if nanosized porosity is present in a significant amount. Pores are classified based on their average size, by the International Union of Pure and Applied Chemistry (IUPAC), in micropores if the pores internal width is below 2 nm, mesopores if it is between 2 and 50 nm, and macropores if the internal width is over 50 nm [17]. Moreover, pores can be open or closed, slit-shaped, i.e., characterized by plane walls, or cylindrical, and the whole porosity can be composed of an ordered network or a disordered set of voids. Crystalline materials like zeolites [18] and metal-organic frameworks [19], for example, possess a regular and well defined system of pores, while amorphous materials, like activated carbons [20] and different classes of polymers [21; 22; 23], possess an interconnected irregular-shaped porosity. Hyper-crosslinked (HCL) polymers are a class of microporous polymers that are prepared by the extensive crosslinking of linear or lightly crosslinked precursor polymers. They can be obtained by a two-step or by a one-pot process, starting from several aromatic monomers [24; 25; 26; 27; 28]. Hyper-crosslinked polymers (HCP) show extremely high surface areas and porosity, low density, outstanding adsorption properties, high chemical, and thermal stability [29]. The first example of HCP, synthesised by [PERSON] and co-workers, was based on polystyrene (HCL PS) [30]. Since then, many researches have focused on HCL PS-based polymers, diversifying, for example, the crosslinking degree of the precursor polymer in order to modulate the HCL PS pore size distribution and SSA (up to \(\sim\)2000 m\({}^{2}\)/g). In addition, various synthetic procedures were explored to obtain highly crosslinked materials in different morphologies. Moreover, the introduction of functionalized monomers or the post-crosslinking chemical modification were considered to impart specific functionality to the HCL PS. Other classes of hyper-crosslinked polymers have been explored more recently. Polysulfone, for example, was hyper-crosslinked through a two-step reaction, consisting into the grafting of a bromomethyl moiety onto the polysulfone benzene rings and the successive hyper-crosslinking through Friedel-Crafts reaction. However, polysulfone shows low activity in the Friedel-Crafts reaction and a high inherent chain flexibility, which both limit the achieving of a high hyper-crosslinking degree, leading to low SSA (\(\sim\)70 m\({}^{2}\)/g) materials [31]. Hyper-crosslinking of polyaniline through a microwave assisted process, instead, allowed for obtaining a material with an SSA of about 1000 m\({}^{2}\)/g and a high adsorption capability towards CO\({}_{2}\) and H\({}_{2}\)[32]. A natural polymer like lignin was also crosslinked by using an external crosslinker, formaldehyde dimethyl acetal (FDA), and, upon a pyrolysis treatment, this material displayed SSA of about 100 m\({}^{2}\)/g and high CO\({}_{2}\)/N\({}_{2}\) selectivity [33]. Nevertheless, when considering their possible wide differentiation in terms of monomer composition, pre- or post-functionalization, and the type of synthetic approach adopted, HCL PS are still the most representative class of high SSA materials.