This dissertation proposes distributed adaptive algorithms exploiting sparsity for parameter and spectrum estimation over sensor networks. Conventional and modified conjugate gradient (CG and MCG) algorithms using consensus and diffusion strategies are presented. Sparsity-aware versions of CG an MCG algorithms using l1 and log-sum penalty functions are developed. The proposed sparsity-aware and non-sparse CG and MCG methods outperform the equivalent variants of the least-mean square (LMS) algorithms in terms of convergence rate and mean square deviation (MSD) at steady state, and have a close performance to the recursive least square (RLS) algorithm. The diffusion CG strategies have shown the best performance, specifically the adapt then combine (ATC) version. Furthermore a distributed alternating mixed discretecontinuous (DAMDC) algorithm to approach the oracle algorithm based on the diffusion strategy for parameter and spectrum estimation over sensor networks is proposed. An LMS type algorithm with the DAMDC proposed technique obtains the oracle matrix in an adaptive way and compare it with the existing sparsity-aware as well as the classical algorithms. The proposed algorithm has an improved performance in terms of MSD. Numerical results show that the DAMDC-LMS algorithm is reliable and can be applied in several scenarios.