The Jiangmen Underground Neutrino Observatory (JUNO) is a next-generation liquid scintillator experiment being built in the Guangdong province in China. JUNO's target mass of 20 kton will be contained in a 35.4 m acrylic vessel, itself submerged in a water pool, under about \SI{700}{\meter} of granite overburden. Surrounding the acrylic vessel are 17612 20'' PMTs and 25600 3'' PMTs. The main goal of JUNO, whose construction is scheduled for completion in 2022, is a 3-4$\sigma$ determination of the neutrino mass ordering (MO) using reactor neutrinos within six years, as well as a precise measurement of $\theta_{12}$, $\Delta m_{21}^2$, and $\Delta m_{31}^2$. JUNO's large target mass, low background, and dual calorimetry, leading to an excellent energy resolution and low threshold, allows for a rich physics program with many applications in neutrino physics. The large target mass will allow for high-statistics solar-, geo-, and atmospheric neutrino measurements. JUNO will also be able to measure neutrinos from galactic core-collapse supernovae, detecting about 10,000 events for a supernova at \SI{10}{\kilo\parsec}, and achieve a 3$\sigma$ discovery of the diffuse supernova neutrino background in ten years. It can also study non-standard interactions e.g. proton decay, indirect dark matter searches, and probe for Lorentz invariance violations. This paper covers this extensive range of non-oscillation topics on which JUNO will be able to shed light.