The building sector is responsible for 39% of process-related greenhouse gas emissions globally, making net- or nearly-zero energy buildings pivotal for reaching climate neutrality. This article reviews recent advances in key options and strategies for converting the building sector to be climate neutral. The evidence from the literature shows it is possible to achieve net or nearly-zero energy building outcomes across the world in most building types and climates with systems, technologies, and skills that already exist, and at costs that are in the range of conventional buildings. Maximizing energy efficiency for all building energy uses is found as central to net zero targets. Jurisdictions all over the world, including Brussels, New York, Vancouver, and Tyrol, have innovated visionary policies to catalyze the success of such buildings, with more than 7 million square meters of nearly-zero energy buildings erected in China alone in the past few years. Since embodied carbon in building materials can consume up to a half of the remaining 1.5°C carbon budget, this article reviews recent advances to minimize embodied energy and store carbon in building materials.