The challenge of determining the ground state energy in quantum chemistry has led to the development of many computational methods, each with their own advantages and disadvantages. In this dissertation, we focus on two such methods - diffusion Monte Carlo (DMC) and the stochastic heatbath configuration interaction (SHCI) method. Both methods are systematically improvable and therefore can, at least in principle, be used to determine the exact energy of any system given enough computational resources. In practice, various approximations must be made to keep the computational cost under control, and determining the exact energy is only possible after controlling for various errors and extrapolating to various limits. We develop several improvements to each method which aid in this process of determining the true energy of chemical systems. In Chapter 2 we focus on DMC. Nonlocal pseudopotentials are often used to remove core electrons to improve computational efficiency. For these systems, we introduce an additional Metropolis-Hastings accept-reject step in the T-moves algorithm which results in lower time-step errors in the total energy and a greatly improved distribution sampled by DMC. The time-step errors in observables which do not commute with the Hamiltonian are especially improved. We also introduce an exact expression for the nonlocal part of the Green's function, for which a linear approximation in the time-step is often used. This leads to only minor improvements, but is straightforward to implement. We then introduce a number of criteria which the ideal reweighting factor should have, and introduce an example of a reweighting factor which meets all criteria. Using this reweighting factor, we show that the time-step error in the total energies of both pseudopotential and all-electron calculations are consistently improved for a variety of systems. In Chapter 3 we present improvements to SHCI. First, we introduce an array called the singles queue which allows us to improve the efficiency of selecting important singly excited Slater determinants. Each element of this array contains an upper bound on the absolute value of the Hamiltonian matrix element between any single excitation involving a given pair of orbitals, which allows us to very efficiently eliminate single excitations which cannot satisfy the SHCI criterion. Second, we introduce a basis-set correction based on range-separated density functional theory (DFT) which aids extrapolation to the complete basis set (CBS) limit. Because SHCI, in common with all other quantum chemistry methods except DMC which works directly in the complete basis limit, typically converges very slowly with respect to the size of the basis, this improvement greatly improves our ability to reach chemical accuracy with SHCI.