A novel hybrid maize variety designated 36Y84 and seed, plants and plant parts thereof, produced by crossing Pioneer Hi-Bred International, Inc. proprietary inbred maize lines. Methods for producing a maize plant that comprises crossing hybrid maize variety 36Y84 with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into 36Y84 through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. This invention relates to the hybrid seed 36Y84, the hybrid plant produced from the seed, and variants, mutants, and trivial modifications of hybrid 36Y84. This invention further relates to methods for producing maize lines derived from hybrid maize variety 36Y84 and to the maize lines derived by the use of those methods.