Electrons in conjugated organic polymers and molecules are strongly correlated since most of these systems are quasi one-dimensional. Experimental evidences include existence of two photons below one photon state, observation of negative spin densities in polyene radicals and qualitatively different behavior of optical gaps in polyenes and closely related symmetric cynanine dyes in the thermodynamic limiy. In this talk, I will introduce the model Hamiltonians for the electron states in conjugated systems. The DMRG method is ideally suited for their study. Modifications to the DMRG method to obtain important low-lying states of the systems and methods of obtaining linear and nonlinear optical response coefficients using the DMRG technique will be discussed [1-4]. Application of the method to the study of a wide variety of conjugated systems will be touched upon [5,7]. I will also discuss some recent applications of wave-packet dynamics in the study of some time-dependent phenomena [8]. References [1] S. Ramasesha, Swapan K Pati, H.R. Krishnamurthy, Z. Shuai and J. L. Br´edas, (1996) “Symmetrized DMRG method for the excited states of Hubbard models”, Phys. Rev. B 54, 7598. [2] Z. Shuai, J. L. Br´edas, Swapan K. Pati and S. Ramasesha, (1998) “Comment on the exciton binding energy in the strong correlation limit of conjugated chains”, Phys. Rev. B 58, 15329. [3] Z. Shuai, J. L. Br´edas, Swapan K. Pati and S. Ramasesha, (1997) “Quantum conﬁnement eﬀects on the ordering of the lowest-lying excited states in conjugated chains”, Phys. Rev. B 56, 9298. [4] Swapan K Pati, S. Ramasesha, Z. Shuai and J. L. Br´edas, (1999) “Dynamic nonlinear optical properties from the symmetrized density matrix renormalization group method”, Phys. Rev. B 59, 14827. [5] C. Raghu, Y. Anusooya Pati and S. Ramasesha, (2002) “A density matrix renormalization group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model”, Phys. Rev. B 66, 035116. [6] S. Mukhopadhyay and S. Ramasesha (2009) “Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method”, J. Chem. Phys. 131, 074111. [7] M. Kumar and S. Ramasesha, (2010) “A DMRG Study of the Low-Lying States of Transverse Substituted Trans-polyacetylene and Trans-polyacetylene”, Phys. Rev. B. 81, 035115 [8] Tirthankar Dutta and S. Ramasesha, (2010) “Double time window targeting technique: Real-time DMRG dynamics in Pariser-Parr-Pople model”, Phys. Rev. B 82, 035115. [9] Simil Thomas, Daniel Garcia, Karen Hallberg and S. Ramasesha "Fused Azulenes: Possible Organic Multiferroics", Phys. Rev. B RC (communicated)