There are several web-pages or blogs that I find very useful, both for research and teaching:

• http://www.hairer.org/index.html

• https://terrytao.wordpress.com/

• https://fabricebaudoin.wordpress.com/

• https://almostsure.wordpress.com/

• https://www.randomservices.org/random/index.html

• https://linbaba.wordpress.com/

• Cambridge Notes taken by Dexter Chua

• Useful materials on Bayesian Filterning and SDEs with many interesting applications in engineering and machine learning  can be found on Simo Särkkä's web page.

• https://personal.ntu.edu.sg/nprivault/

For the young students aiming a career in mathematics (but not necessarily), some useful advice could also be found at some blogs mentioned above, e.g.:  "Ten lessons I wish I had been taught", by Gian-Carlo Rota, or "Advice on writing papers" by Terence Tao.