The physics and chemistry of plasma-surface interaction is a broad domain relevant to various applications and several natural processes, including plasma etching for microelectronics fabrication, plasma deposition, surface functionalization, nanomaterial synthesis, fusion reactors, and some astrophysical and meteorological phenomena. Due to their complex nature, each of these processes are generally investigated in separate subdomains, which are considered to have their own theoretical, modeling and experimental challenges. In this review, however, we want to emphasize the overarching nature of plasma-surface interaction physics and chemistry, by focusing on the general strategy for its computational simulation. In the first half of the review, we provide a menu card with standard and less standardized computational methods to be used for the multiscale modeling of the underlying processes. In the second half, we illustrate the benefits and potential of the multiscale modeling strategy with a case study of Si and SiO2 etching by fluorocarbon plasmas, and identify the gaps in knowledge still present on this intensely investigated plasma-material combination, both on a qualitative and quantitative level. Remarkably, the dominant etching mechanisms remain the least understood. The resulting new insights are of general relevance, for all plasmas and materials, including their various applications. We therefore hope to motivate computational and experimental scientists and engineers to collaborate more intensely on filling the existing gaps in knowledge. In this way, we expect that research will overcome a bottleneck stage in the development and optimization of multiscale models, and thus the fundamental understanding of plasma-surface interaction. TABLE OF CONTENTS wanderlust 3.3.2 Application-specific methods -specialize in the impossible 3.3.3 Machine learning -brainstorming by artificial intelligence 3.3.4 Plasma sheath modeling -matter's aura explained 3.4 Multiscale measuring -because nature is still the best simulation tool 4. PLASMA ETCHING -FROM SCRATCHING THE SURFACE TO GOING IN DEPTH 4.1 The multiscale plasma etching model -one example to represent them all 4.1.1 The need for a bottom-up approach -message in a bottleneck 4.1.2 Hybrid Plasma Equipment Model -example of a hybrid macroscale method 4.1.3 Plasma sheath module -example of a semi-analytical sheath method 4.1.4 Surface kinetics module -example of a deterministic description 4.1.5 Monte Carlo Feature Profile Model -example of a kinetic Monte Carlo method 4.1.6 Experimental benchmarking of the working principle -examples of multiscale measuring 4.1.7 Reactor geometry and operating conditions -example of a case study 4.2 How to implement the surface processes -example of atomistic modeling and measuring data 4.2.1 Elementary plasma-surface mechanisms -simplicity is the ultimate sophistication 4.2.2 Design of the surface chemistry set -a mosaic of quantum data 4.3 Benchmarking the simulation model -bringing uncertainties to the surface 5.