The recent simultaneous research expansion of machine learning (ML) and mobile computing has given birth to the concept of Federated Learning (FL). FL downscales ML's enormous computation power requirement by delegating parts of learning tasks to smaller devices using the devices' own dataset. Results of these bits then proceed to be aggregated to produce a global model. Blockchain, a (semi-)decentralized distributed ledger, enhances FL in reliability, security, correctness, and availability. Nevertheless, a plain blockchain-based FL (BFL) is not always ideal in mobile settings: mobile devices have limited resources to process blockchain routines and training. Plain BFL also relies on wireless connection which is often unstable. In addition, the heterogeneous nature of these devices cannot guarantee optimal model quality. Thus, this survey covers issues in mobile BFL and recent works which give effort to solving the problems and identifies further research potentials in this field. At the end, this work offers a hypothetical prototype of an ideal mobile-based BFL (MBFL).