Low density expanded and extruded thermoplastic polymer foams are obtained using an environmentally benign non-VOC and non-HAP methyl formate as a blowing agent. The blowing agent can be a blend further including at least one co-blowing agent, preferably an environmentally friendly species (e.g., non-VOC and/or non-HAP). The co-blowing agent is either a physical co-blowing agent (e.g. an inorganic agent, a hydrocarbon, a halogenated hydrocarbon, a hydrocarbon with polar, functional group(s), water or any combination thereof), or a chemical co-blowing agent, or combinations thereof. The thermoplastic polymer foam can be an alkenyl aromatic polymer foam, e.g. a polystyrene foam. The blowing agent blend can include any combination of methyl formate and one or more co-blowing agents. The methyl formate-based blowing agent blends produce stable foams for various applications, including containers, packaging systems, as well as insulation boards and building materials. Processes for the preparation of such foams are also provided.