Curcumin (CCM) is one of the most frequently explored plant compounds with various biological actions such as antibacterial, antiviral, antifungal, antineoplastic, and antioxidant/anti-inflammatory properties. The laboratory data and clinical trials have demonstrated that the bioavailability and bioactivity of curcumin are influenced by the feature of the curcumin molecular complex types. Curcumin has a high capacity to form molecular complexes with proteins (such as whey proteins, bovine serum albumin, β-lactoglobulin), carbohydrates, lipids, and natural compounds (e.g., resveratrol, piperine, quercetin). These complexes increase the bioactivity and bioavailability of curcumin. The current review provides these derivatization strategies for curcumin in terms of biological and physico-chemical aspects with a strong focus on different type of proteins, characterization methods, and thermodynamic features of protein–curcumin complexes, and with the aim of evaluating the best performances. The current literature review offers, taking into consideration various biological effects of the CCM, a whole approach for CCM-biomolecules interactions such as CCM-proteins, CCM-nanomaterials, and CCM-natural compounds regarding molecular strategies to improve the bioactivity as well as the bioavailability of curcumin in biological systems.