Application-specific requirements for future lighting, displays and photovoltaics will include large-area, low-weight and mechanical resilience for dual-purpose uses such as electronic skin, textiles and surface conforming foils. Here we demonstrate polymer-based photovoltaic devices on plastic foil substrates less than 2 μm thick, with equal power conversion efficiency to their glass-based counterparts. They can reversibly withstand extreme mechanical deformation and have unprecedented solar cell-specific weight. Instead of a single bend, we form a random network of folds within the device area. The processing methods are standard, so the same weight and flexibility should be achievable in light emitting diodes, capacitors and transistors to fully realize ultrathin organic electronics. These ultrathin organic solar cells are over ten times thinner, lighter and more flexible than any other solar cell of any technology to date.