The chapter introduces the principle of coding in the signal space, which follows from Shannon's analysis of waveform Gaussian channels subject to input constraints. It highlights the early design of communication systems, which focused separately on modulation and error-correcting codes. The perspective of signal-space coding, though not overlooked by information theorists, was brought back into focus by Imai and Ungerböck's pioneering work on coded modulation. Bit-Interleaved Coded Modulation (BICM) is introduced as a pragmatic approach that combines the benefits of both worlds: it leverages the signal-space coding perspective while allowing for the use of powerful families of binary codes with various modulation formats. BICM avoids the complex and less flexible design typically associated with coded modulation. It is widely used in modern systems that achieve high spectral efficiency, such as DSL, Wireless LANs, WiMax, and their evolutions, as well as systems based on low-spectral-efficiency orthogonal modulation. BICM is the *de-facto* general coding technique for waveform channels. The chapter reviews the theoretical foundations of BICM under the unified framework of error exponents for mismatched decoding. It covers the capacity, cutoff rate, and error exponents of BICM, including a wideband regime characterization. The error probability analysis of BICM is examined, focusing on the union bound and improved bounds. iterative decoding of BICM is discussed, including extrinsic information transfer charts, density evolution, and the area theorem. The chapter also presents improved schemes and their design techniques. Finally, it provides an overview of applications of BICM beyond the classical coherent Gaussian channel, such as non-coherent demodulation, block-fading, MIMO, optical communication, and exponential-noise channels.The chapter introduces the principle of coding in the signal space, which follows from Shannon's analysis of waveform Gaussian channels subject to input constraints. It highlights the early design of communication systems, which focused separately on modulation and error-correcting codes. The perspective of signal-space coding, though not overlooked by information theorists, was brought back into focus by Imai and Ungerböck's pioneering work on coded modulation. Bit-Interleaved Coded Modulation (BICM) is introduced as a pragmatic approach that combines the benefits of both worlds: it leverages the signal-space coding perspective while allowing for the use of powerful families of binary codes with various modulation formats. BICM avoids the complex and less flexible design typically associated with coded modulation. It is widely used in modern systems that achieve high spectral efficiency, such as DSL, Wireless LANs, WiMax, and their evolutions, as well as systems based on low-spectral-efficiency orthogonal modulation. BICM is the *de-facto* general coding technique for waveform channels. The chapter reviews the theoretical foundations of BICM under the unified framework of error exponents for mismatched decoding. It covers the capacity, cutoff rate, and error exponents of BICM, including a wideband regime characterization. The error probability analysis of BICM is examined, focusing on the union bound and improved bounds. iterative decoding of BICM is discussed, including extrinsic information transfer charts, density evolution, and the area theorem. The chapter also presents improved schemes and their design techniques. Finally, it provides an overview of applications of BICM beyond the classical coherent Gaussian channel, such as non-coherent demodulation, block-fading, MIMO, optical communication, and exponential-noise channels.