Interacting time and space scales are universal. They frequently go hand in hand with coupled phenomena which can be observed in nature and man-made systems. Such multiscale coupled phenomena are fundamental to our knowledge about all the systems surrounding us, ranging from such global systems as the climate of our planet, to such tiny ones as quantum dots, and all the way down to the building blocks of life such as nucleic acid biological molecules. In this talk we will provide an overview of some coupled multiscale problems that we face in studying physical, engineering, and biological systems. We will start from considering tiny objects, known as low dimensional nanostructures, and will give examples on why the nanoscale is becoming increasingly important in the applications affecting our everyday lives. By using fully coupled mathematical models, we will show how to build on the previous results in developing a new theory, while analyzing the influence of coupled multiscale effects on properties of these tiny objects. We will also talk about coupled multiscale problems in studying biological structures constructed from ribonucleic acid. As compared to deoxyribonucleic acid and some other bio-molecules, ribonucleic acid offers not only a much greater variety of interactions but also great conformational flexibility, making it an important functional material in many bioengineering and medical applications. Examples of numerical simulations of such biological structures will be shown, based on our developed coarse-grained methodologies.