High optical resolution in microscopy usually goes along with costly hardware components, such as lenses, mechanical setups and cameras. Several studies proved that Single Molecular Localization Microscopy can be made affordable, relying on off-the-shelf optical components and industry grade CMOS cameras. Recent technological advantages have yielded consumer-grade camera devices with surprisingly good performance. The camera sensors of smartphones have benefited of this development. Combined with computing power smartphones provide a fantastic opportunity for "imaging on a budget". Here we show that a consumer cellphone is capable of optical super-resolution imaging by (direct) Stochastic Optical Reconstruction Microscopy (dSTORM), achieving optical resolution better than 80 nm. In addition to the use of standard reconstruction algorithms, we used a trained image-to-image generative adversarial network (GAN) to reconstruct video sequences under conditions where traditional algorithms provide sub-optimal localization performance directly on the smartphone. We believe that "cellSTORM" paves the way to make super-resolution microscopy not only affordable but available due to the ubiquity of cellphone cameras.