The microscopic and molecular-level characterization and understanding of excited states properties and dynamics plays an important role in modern scientic research. Tremendous examples can be found in photovoltaics, photocatalysis, spintronics, and plasmonics. Over the past several decades, despite progress towards this direction through experimental approaches, such as crystallography and spectroscopy, it is important to realize that many chemical transformations, especially when associated with excited states, are still dicult to be precisely detected and accurately characterized in experiments. One typical example is optically forbidden (dark) states, which are experimentally barely accessible, but very often determine the excited state dynamics. Fortunately, quantum chemical calculations of such excited states are usually able to provide accurate and predictive information, and do indeed contribute to the fundamental understanding of excited state properties and dynamics. To describe excited states properly with quantum mechanics, essentially, one needs to adopt a quantum chemical method that is able to describe electron correlations towards "chemical accuracy" (1 kcal/mol). Among all available quantum chemical methods, the density functional theory/time-dependent density functional theory (DFT/TDDFT) are extremely popular. Their favorable trade-off between accuracy and computational cost has made them standard technique in most branches of chemistry and materials science. However, DFT/TDDFT results depend on the specic exchange-correlation (XC) functional adopted. The wave-function-based ab initio methods, on the other hand, can be systematically improved to provide reliable results. A typical example is the coupled-cluster (CC) model, in which various correlation effects can be categorized according to the rank of excitations included in the approximate form of the cluster and excitation operators, and its accuracy can then be systematically improved by including higher excitations explicitly or perturbatively. In particular, the CC model with single and double excitations corrected by perturbative triples, a.k.a. CCSD(T), has been recognized as the "gold standard" for computational chemistry. However, these wave-function-based methods always suffered from very high computational cost (e.g. the canonical procedure of CCSD(T) scales as O(N7) with N the number of basis functions representing system size), which precludes them from being applied to large systems. The main objective of this work is to develop quantum chemical methods that provide better trade-off between accuracy and eciency for the description of electron correlations in some electron excitation scenarios where conventional methods may encounter problems. Several newly developed approximations and algorithms based on DFT, TDDFT, and CC will be presented in the following chapters. The applications of these methods include the computations of excitation energy, excited state wave function, and excited state dynamics. The structure of this thesis is as follows. In Chapter 1, the theoretical background of quantum chemical methods for the study of excited states is given. The emphasis is on DFT, TDDFT and CC. Chapter 2 describes a guided self-consistent-field (SCF) method developed in this work. The working procedure of this method is presented within DFT framework. The application of this method to the computation of the d-d transition energies in some metal complexes is discussed. In Chapter 3, a factorization method is introduced to deal with states coupling driven by pure electron-electron interaction. In combination with DFT and TDDFT technique, its application in estimating the transition rate of a spin- fliped Auger process in large CdSe quantum dots is discussed. Chapter 4 discusses the real-time TDDFT method. The case study is focusing on the exciton dynamics in a two-silver-atomic-chain prototype system that goes beyond the capability of canonical models of electronic energy transfer. In Chapter 5 a variant of the equation-of-motion CC (EOM-CC) method aiming at solving interior eigenpairs of the EOM Hamiltonian matrix is discussed. A benchmark of this method is done by computing the K-edge core excitation energies of carbon, oxygen, nitrogen, and sulfur in some molecules.