The study of knots in the $3$-space, has a long story. A mathematical framework for this study formed in 19th century and some interesting theorems were proved in the first half of 20th century. Nevertheless, perhaps the more important developments occurred towards the end of 20th century, as well as the past years of the new millennium. We will review some of the major steps, including some of the new tools developed for the study of knots and links, as well as some open questions in this area with relatively simple statements.