We introduce the basic concepts of two-dimensional electronic spectroscopy (2DES) and a general theoretical framework adopted to calculate, from first principles, the nonlinear response of multi-chromophoric systems in realistic environments. Specifically, we focus on UV-active chromophores representing the building blocks of biological systems, from proteins to nucleic acids, describing our progress in developing computational tools and protocols for accurate simulation of their 2DUV spectra. The roadmap for accurate 2DUV spectroscopy simulations is illustrated starting with benchmarking of the excited-state manifold of the chromophoric units in a vacuum, which can be used for building exciton Hamiltonians for large-scale applications or as a reference for first-principles simulations with reduced computational cost, enabling treatment of minimal (still realistic) multi-chromophoric model systems. By adopting a static approximation that neglects dynamic processes such as spectral diffusion and population transfer, we show how 2DUV is able to characterize the ground-state conformational space of dinucleosides and small peptides comprising dimeric chromophoric units (in their native environment) by tracking inter-chromophoric electronic couplings. Recovering the excited-state coherent vibrational dynamics and population transfers, we observe a remarkable agreement between the predicted 2DUV spectra of the pyrene molecule and the experimental results. These results further led to theoretical studies of the excited-state dynamics in a solvated dinucleoside system, showing that spectroscopic fingerprints of long-lived excited-state minima along the complex photoinduced decay pathways of DNA/RNA model systems can be simulated at a reasonable computational cost. Our results exemplify the impact of accurate simulation of 2DES spectra in revealing complex physicochemical properties of fundamental biological systems and should trigger further theoretical developments as well as new experiments.