Floating-gate devices occupy a pivotal position in contemporary electronic systems, owing to their versatile capabilities in nonvolatile memory storage, analog circuit design, and emerging applications in neuromorphic computing. These devices leverage a distinctive floating-gate structure isolated from the surrounding circuitry, enabling the storage and manipulation of charge. The ability to retain charges even without external power makes them ideal for the applications requiring persistent data storage. This review explores the fundamental principles of floating-gate devices, focusing on their application in emerging logic devices combining floating-gate structures such as (i) reconfigurable logics, (ii) multi-valued logics, (iii) neuromorphic logics, and (iv) in-sensor computing. Various types of floating-gate devices for these new concept logics are examined, highlighting their key characteristics and advantages. Potential solutions and future research directions are also discussed. Based on the comprehensive review of recent three-year studies, we aim to provide an overview of floating-gate-based logic devices, emphasizing their significance in modern electronics and their potential to enable innovative applications in the fields of logic and memory devices.