New solar extreme-ultraviolet (EUV) irradiance observations from the NASA Solar Dynamics Observatory (SDO) EUV Variability Experiment provide full coverage in the EUV range from 0.1 to 106 nm and continuously at a cadence of 10 s for spectra at 0.1 nm resolution and even faster, 0.25 s, for six EUV bands. These observations can be decomposed into four distinct characteristics during flares. First, the emissions that dominate during the flare's impulsive phase are the transition region emissions, such as the He II 30.4 nm. Second, the hot coronal emissions above 5 MK dominate during the gradual phase and are highly correlated with the GOES X-ray. A third flare characteristic in the EUV is coronal dimming, seen best in the cool corona, such as the Fe IX 17.1 nm. As the post-flare loops reconnect and cool, many of the EUV coronal emissions peak a few minutes after the GOES X-ray peak. One interesting variation of the post-eruptive loop reconnection is that warm coronal emissions (e.g., Fe XVI 33.5 nm) sometimes exhibit a second large peak separated from the primary flare event by many minutes to hours, with EUV emission originating not from the original flare site and its immediate vicinity, but rather from a volume of higher loops. We refer to this second peak as the EUV late phase. The characterization of many flares during the SDO mission is provided, including quantification of the spectral irradiance from the EUV late phase that cannot be inferred from GOES X-ray diagnostics.