To do this, you need to follow the discoveries and news from the world of science. Therefore, just at your leisure, read articles from any popular science publication (my favorites are N + 1 and PostNauka). There are also good Naked Scince and Popular Mechanics (both in print).
It depends on what you mean by currents. If you are simply interested in modern research and new discoveries, the news sites in the "science" section will help you. There it is often told in simple language what exactly was discovered, where, how, and what it does
If you are interested in something more complex and in-depth, visit Habr. There are a lot of articles with formulas, research, detailed analysis of various technologies. Moreover, topics for discussion are very different
If you are wondering what science is doing now, choose the one you need and find in Wikipedia "List of unsolved problems% name of science%". For example, physics. And you will be able to look at what scientists are now struggling with, what they are studying, and what they cannot study. There, as a rule, there are links to an article with resolved "unsolved" issues of this science, which can also be read about. But keep in mind right away that this is perhaps the most difficult topic, because such articles on Wikipedia usually do not know the concept of "low entry threshold" at all. It is there immediately maximum and basically goes into calculations, formulas and conditions. However, the basic concepts and ideas can be gleaned
Traditionally, sorting according to the difficulty of mastering and options for solving the issue. Choose which one you like best. I am personally for the third, but maybe I just have the nature of a dreamer