Expanded and extruded polyolefin foams are obtained using environmentally benign non-VOC 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), which is either a physical co-blowing agent (e.g. an inorganic agent, a hydrocarbon, a halogenated hydrocarbon, a hydrocarbon with polar, functional group(s) or any combination thereof), or a chemical co-blowing agent, or combinations thereof. The blowing agent blend can include any combination of methyl formate and one or more co-blowing agents. The polymer foam can include polyethylene, polypropylene or a combination thereof. The methyl formate-based blowing agent blends produce stable foams for various applications, including containers, packaging systems, as well as for insulation and protective cushioning. Processes for the preparation of such foams are also provided.