Biological cells, in some sense, are all about topology: Biomembranes separating different volumes from one another, ions or even macromolecules having to cross these membranes in controlled fashion through membrane pores; or certain proteins moving along the DNA to find their target sequence instead of searching for this site in the full 3-dimensional cell volume. Even on the single biopolymer level, topology is an essential ingredient: Intriguingly, in bacteria DNA occurs knotted, i.e., in a state topologically different from a simply connected ring. It is a key question to understand the statistical behaviour of such knotted DNA to understand a number of physiological processes having to overcome this knottedness, or to quantify results from DNA separation techniques such as electrophoresis, in which the knottedness influences the mobility. At the same time, double-stranded DNA continuously opens up floppy single-stranded bubbles, which fluctuate in size, exposing the single Watson-Crick bases to binding proteins. Again, statistical mechanical tools can be employed to examine the bubble dynamics. Here, we introduce some recent results on DNA knots and bubble fluctuations.