This paper describes challenges, solutions, and prospects for data recovery in multilayer magnetic recording (MLMR)—the vertical stacking of magnetic media layers to increase information storage density. To this end, the channel model for MLMR is discussed. Data recovery is described in terms of the readback stage followed by equalization and then detection. We illustrate how deep neural networks (DNNs) can be used to design systems for equalization and detection for MLMR. We show that such DNN-based systems outperform the conventional baseline and provide a good trade-off between complexity and performance. To achieve additional density gains, several prospective methods are discussed. On a physical level, the selective reading of tracks on different layers can be achieved by resonant reading. Resonant reading promises reduced interference from different layers, enabling higher storage densities. Regarding the signal processing, DNNs can be used to estimate the media noise and iteratively exchange soft-bit information with the decoder. Also, to ameliorate partial erasures, an auto-encoder-based system is proposed as a modulation coding scheme.