Nuclear energy is based on heat released by atomic (uranium) fission reactions which proceed via a chain reaction. Various technologies compete in the sector, mainly divided into light water reactors (LWRs), more popular, and heavy water reactors (HWRs). The main difference between them is that LWRs need enriched uranium, while HWRs can use natural uranium.
The development is now at the third plus generation, focusing mainly on safety measures, such as simplified core design and natural convection-driven cooling in case of loss-of-coolant (LOCA) incident.
Simplifying, core design measures include: natural convention air design (uses air cooling), gravity drain water tank (moved water on top of reactor, so no need for pumps), water film evaporation, outside cooling air intake (another measure to use external atmospheric temperature for cooling) and steel containment vessel (better protection). Simplified core design is aimed to reduced complexity and consequently increase reliability.
The main problem for nuclear resides mainly in the economics of a project, needing high capex and having long rate-of-investment; spent fuel handling and storage; and nuclear proliferation (atomic bombs). Fusion can be a player in the future, mainly due to better safety measure (there cannot be a core melt-down) and shorter (10s-100s) lived activated reactor components (Tynan, The future of Nuclear Energy: Future of Energy, 2014)