Touch is a complex sensing modality owing to large number of receptors (mechano, thermal, pain) nonuniformly embedded in the soft skin all over the body. These receptors can gather and encode the large tactile data, allowing us to feel and perceive the real world. This efficient somatosensation far outperforms the touch-sensing capability of most of the state-of-the-art robots today and suggests the need for neural-like hardware for electronic skin (e-skin). This could be attained through either innovative schemes for developing distributed electronics or repurposing the neuromorphic circuits developed for other sensory modalities such as vision and audio. This Review highlights the hardware implementations of various computational building blocks for e-skin and the ways they can be integrated to potentially realize human skin-like or peripheral nervous system-like functionalities. The neural-like sensing and data processing are discussed along with various algorithms and hardware architectures. The integration of ultrathin neuromorphic chips for local computation and the printed electronics on soft substrate used for the development of e-skin over large areas are expected to advance robotic interaction as well as open new avenues for research in medical instrumentation, wearables, electronics, and neuroprosthetics.