Spectral sideband formation is a fundamental phenomenon in soliton fiber lasers, arising from multiple mechanisms. The most recognized are Kelly sidebands, generated from the linear interference between a soliton and dispersive waves due to periodic perturbations in the cavity. Modulation instability (MI) is another key driver, creating sidebands in both anomalous and normal dispersion regimes through conventional and cavity-aided MI. Furthermore, forced periodic variations in soliton parameters like energy or pulse width can induce additional sidebands, while nonlinear interactions between orthogonally polarized components generate polarization instability-induced sidebands. Studying these sidebands provides critical insight into soliton dynamics, formation, and stability, which is essential for optimizing ultrafast lasers for telecommunications and high-power applications. This examination covers the properties of these various sidebands and discusses their significant influence on soliton operation. The text begins with a theoretical description of sidebands predicted for scalar and coupled nonlinear Schrödinger equations, summarizes key research results, and concludes with a discussion on future research directions.