Platforms with curved side edges and gas turbine engine systems involving such platforms

Platforms with curved side edges and gas turbine engine systems involving such platforms are provided. In this regard, a representative airfoil assembly for a gas turbine engine includes: a platform having a gas path side, a non-gas path side, a leading edge, a trailing edge, a first side edge extending between the leading edge and the trailing edge and exhibiting a first curve along a length thereof, and a second side edge extending between the leading edge and the trailing edge and exhibiting a second curve along a length thereof; and an airfoil extending from the gas path side of the platform; the platform and the airfoil exhibiting a unitary construction such that a continuous exterior surface blends from the airfoil to the platform.