The paper presents a framework for models where electroweak symmetry breaking is driven by a light composite Higgs boson, emerging as a pseudo-Goldstone boson from a strongly-interacting sector. The key parameters are $ m_{\rho} $, the mass scale of new resonances, and $ g_{\rho} $, their coupling. An effective low-energy Lagrangian approach is useful for LHC and ILC phenomenology below $ m_{\rho} $. Two classes of operators are identified: those sensitive to the new strong force and those sensitive to resonance spectra. Phenomenological prospects include high-energy longitudinal vector boson scattering, strong double-Higgs production, and anomalous Higgs couplings. The paper discusses the possibility that the top quark could also be a composite object in the strong sector. The paper introduces the Strongly-Interacting Light Higgs (SILH) scenario, where the Higgs is an effective field from new dynamics at a scale not much larger than the Fermi scale. The structure of the theories involves a new sector with parameters $ g_{\rho} $ and $ m_{\rho} $, and the Higgs is assumed to belong to this sector. The SM vector bosons and fermions are weakly coupled to the strong sector. The Higgs doublet is an exact Goldstone boson in the G/H coset space of a spontaneously broken symmetry. The gauging of $ SU(2) \times U(1)_Y $ and non-zero Yukawas break the Goldstone symmetry, leading to terms in the action not invariant under the symmetry. The Higgs mass is softened by the new dynamics, and the Higgs mass parameter scales like $ (\alpha_{SM}/4\pi)m_{\rho}^2 $. The paper discusses the structure of the SILH and its effective Lagrangian, which includes dimension-6 operators involving Higgs and gauge fields. These operators are derived from the low-energy effective theory and include terms like $ \partial^{\mu}(H^{\dagger}H)\partial_{\mu}(H^{\dagger}H) $, $ H^{\dagger}\overleftrightarrow{D^{\mu}}H H^{\dagger}\overleftrightarrow{D_{\mu}}H $, and others. The coefficients of these operators are determined by the $ \sigma $-model structure and the symmetry breaking terms. The paper also discusses the implications of these operators for Higgs and gauge boson interactions, including the $ \rho $ parameter and the $ \widehat{S} $ parameter. The paper relates the SILH to explicit models, such as the Georgi-Kaplan model and Holographic Goldstones, which belong to the first class where the Higgs potential is saturated by quantum effects at the scale $ m_{\rho} $. Other models, like Little HThe paper presents a framework for models where electroweak symmetry breaking is driven by a light composite Higgs boson, emerging as a pseudo-Goldstone boson from a strongly-interacting sector. The key parameters are $ m_{\rho} $, the mass scale of new resonances, and $ g_{\rho} $, their coupling. An effective low-energy Lagrangian approach is useful for LHC and ILC phenomenology below $ m_{\rho} $. Two classes of operators are identified: those sensitive to the new strong force and those sensitive to resonance spectra. Phenomenological prospects include high-energy longitudinal vector boson scattering, strong double-Higgs production, and anomalous Higgs couplings. The paper discusses the possibility that the top quark could also be a composite object in the strong sector. The paper introduces the Strongly-Interacting Light Higgs (SILH) scenario, where the Higgs is an effective field from new dynamics at a scale not much larger than the Fermi scale. The structure of the theories involves a new sector with parameters $ g_{\rho} $ and $ m_{\rho} $, and the Higgs is assumed to belong to this sector. The SM vector bosons and fermions are weakly coupled to the strong sector. The Higgs doublet is an exact Goldstone boson in the G/H coset space of a spontaneously broken symmetry. The gauging of $ SU(2) \times U(1)_Y $ and non-zero Yukawas break the Goldstone symmetry, leading to terms in the action not invariant under the symmetry. The Higgs mass is softened by the new dynamics, and the Higgs mass parameter scales like $ (\alpha_{SM}/4\pi)m_{\rho}^2 $. The paper discusses the structure of the SILH and its effective Lagrangian, which includes dimension-6 operators involving Higgs and gauge fields. These operators are derived from the low-energy effective theory and include terms like $ \partial^{\mu}(H^{\dagger}H)\partial_{\mu}(H^{\dagger}H) $, $ H^{\dagger}\overleftrightarrow{D^{\mu}}H H^{\dagger}\overleftrightarrow{D_{\mu}}H $, and others. The coefficients of these operators are determined by the $ \sigma $-model structure and the symmetry breaking terms. The paper also discusses the implications of these operators for Higgs and gauge boson interactions, including the $ \rho $ parameter and the $ \widehat{S} $ parameter. The paper relates the SILH to explicit models, such as the Georgi-Kaplan model and Holographic Goldstones, which belong to the first class where the Higgs potential is saturated by quantum effects at the scale $ m_{\rho} $. Other models, like Little H