Having spent a lot of time with popular science, I am generally exposed to topics that are either very well-developed (like calculus) or have a very rich history (like geometry). Authors tend to avoid very "trendy" or "exotic" topics since theories/concepts in there are generally less widely accepted.
This got me wondering, what are some areas of mathematics that has only started developing within the past 10-15 years? Are there any up-and-coming areas of mathematics that most mathematicians are very hopeful and excited about? And what are some of the lesser known areas of mathematics (and why are they not as well-known)?