Natural complex mixtures are constituents of food, flavor, and fragrance products, with analysis of these matrices being carried out in ^[1][40] (Figure 1 and Table 1).

One-dimensional chromatography does not provide sufficient selectivity for the separation of the complex, as there are problems of overlapping peaks, variation in selectivity, or even when the components are present in trace amounts, hampering the selectivity ^[2][3][41,42]. On the contrary, multidimensional chromatography provides an advanced pre-separation effect before analyte separation and quantification, ultimately overcoming the problems related to peak overlapping and trace element detection ^[4][5][43,44].

A large number of food products, flavorings, and fragrances consist of chiral compounds that, on detection, present overlapping peaks and selectivity problems. The distribution of enantiomers is useful for the identification of adulterants, controlling the fermentation process and storage effects. GC–GC can be used for the enantiomeric determination of these products, but pre-selection is crucial due to overlapping peaks. The pre-chiral columns are being used before the main chiral column just to avoid overlapping peaks. This method is used to determine products’ authenticity ^[6][45].

Multidimensional HPLC has high separation power; hence it is used for the separation of complex molecules ^[7][8][18,46]. Heart-cut, on-column concentration, or trace enrichment are different types of techniques used to promote the application of multidimensional HPLC ^[9][47]. Using multidimensional HPLC, the researchers have been able to determine the levels of complex B vitamins in protein food, on-column vitamin concentrations in food matrixes, molasses sugars, malathion in tomato plants, lemonin in grapefruit peels, and other polar pesticides, with detection limits being as low as 0.1 g/L ^[10][11][48,49].

Multidimensional chromatography is used widely in the field of the biomedical and pharmaceutical industry due to the complex nature of the analyte and decreased amount present in the biological matrix ^[12][13][14][50,51,52] (Figure 1). High selectivity and accurate systems are needed with high reliance to determine such compounds ^[15][16][53,54].

LC is well established in these industries and very well adopted, so LC remains a component for separation and quantification purposes, along with other systems. Online and offline approaches are being used for coupling systems, where the online approach provides greater accuracy and precision along with shorter analysis time ^[17][55].

Charged, polar, thermolabile, non-volatile, and high-molecular-weight compounds are just some of the clinically relevant chemicals that can be directly examined by LC. Antibiotics, retinoids, methotrexate, codeine, psilocin, and almokalant have all been studied using this method, as well as anabolic steroids, morphine, and clozapine ^[18][56].

Industrial chemicals and associated materials have also been subjected to multidimensional chromatography analysis (Figure 1). Coal tar, antiknock additives in gasoline, light hydrocarbons, trihaloalkanes and trihaloalkenes in industrial solvents, soot, particle extracts, and different industrial compounds that may be found in gasoline and oil samples have been studied via multidimensional chromatography ^[19][57].

The rapid identification of polymer additives, such as antioxidants, lubricants, flame retardants, waxes, and UV stabilizers was made possible by a multidimensional system using capillary SEC–GC–MS ^[20][58]. Chemical additives, such as hydrocarbons and alcohols, for example, may not only be analyzed in the context of polymer chemistry but also in the context of food chemistry using the same methodologies. The study of polyaromatic hydrocarbons in food oils has also proven very important. Moreover, a polystyrene matrix has been employed for the investigation of polymer additives using SEC and GC ^[21][59].

Environmental analysis relies heavily on multidimensional chromatography. The wide range of polarity of the constituents and a large number of isomers or congeners with similar or equal retention properties make it impossible to separate environmental samples using a single chromatographic approach (Table 1). Polycyclic aromatic hydrocarbons (PAHs), pesticides, and halogenated chemicals are all persistent organic pollutants that can be found in the air, water, soil, and sediment, and multidimensional chromatography has been used to analyze such contaminants ^[22][60]. Among them are polychlorinated dibenzo-dioxins, dibenzofurans, polychlorinated biphenyl, terphenyls, naphthalene, alkanes, organochlorine insecticides, and the brominated flame retardants, polybrominated biphenyls and polybrominated diphenyl ethers, which are some of the most representative ^[23][61].

Analyses in forensic and toxicological sciences involve the identification of complexes that signal sickness, poisons, and a wide range of unlawful acts as examples ^[24][62] (Figure 1). Tissues, urine, plasma, serum, hair, arson debris, and fragments of other objects are often discovered to contain analytes ^[25][26][63,64]. For such purposes, LC–GC has been used for the analysis of numerous toxic complexes in biological samples, such as plasma and tissues, whereas GC–GC has been used for complex samples with exceptional selectivity. For example, organic pesticides and polychlorinated biphenyls (PCBs) may be separated and analyzed using online LC–GC, which can also be used for lipid matrices. In addition, the analysis of illicit growth hormones in corned beef can be performed using LC linked to two-dimensional GC ^[27][65]. Specifically, LC–LC has found its extensive use for the analysis of biological matrices, while GC–GC has special applications in determining drugs with specific selectivity. More recently, micellar HPLC has been used for the analysis of cardiovascular drugs from urine ^[28][66].

Multidimensional LC has also been used to determine ursodeoxycholic acid and its conjugates in serum, while multidimensional GC is used to separate derived urinary organic acids that are indicative of metabolic diseases, phenylketonuria, tyrosinemia, and others. Additionally, two-dimensional GC is used for the determination of 2,2,3,3,4,6-hexachlorobiphenyl in milk ^[29][67]. Food products often contain complex matrix interferences, such as emulsifiers, thickeners, stabilizers, pigments, antioxidants, and others, making it difficult to analyze the analytes of interest. As such, multidimensional GC coupled with infrared or mass spectroscopy may be used to improve the outcomes (Figure 1 and Table 1) ^[30][68].