Nuclear war is potentially the primary near-term technological existential risk. Nuclear war would probably not cause human extinction through the direct damage of an exchange. Rather, researchers are concerned about the potential for a nuclear winter: firestorms caused by the explosions could release particulate matter into the atmosphere, causing significant global cooling which would last for several years. This cooling would disrupt global agriculture, which might kill even more people than the initial exchange.
However, there is some disagreement about how climate systems would react to the particulate matter and how much soot would actually be created (modern cities are potentially less vulnerable to firestorms than those during the cold war). As a result, it is unclear whether nuclear war poses an existential risk or a non-existential global catastrophic risk.
Cotton-Barratt, Owen et al. 2016. Global catastrophic risks.
A report focusing on risks from nuclear war, as well as other types of global catastrophic risk.
Open Philanthropy Project. 2016. Nuclear weapons policy.
A report exploring possible interventions to address risks from nuclear war.