In this thesis, I focus on the physical and chemical evolution at the earliest stages of low-mass star formation. I report results from the Spitzer Space Telescope and molecular line observations of 9 species toward the dark cloud L43, a survey of 10 Class 0 and 6 Class I protostars with 8 molecular lines, and a survey of 9 Very Low Luminosity Objects (VeLLOs) with 11 molecular lines. From the observational results, CO depletion is extensively observed with C¹⁸O(2-1) maps. A general evolutionary trend is also seen toward the Class 0 and I samples: higher deuterium fractionation at higher CO depletion. For the VeLLO candidates and starless cores with N₂D⁺(3-2) detection, we found the deuterium ratio of N₂D⁺/N₂H⁺ is higher comparing with the Class 0 and I samples. We use DCO⁺(3-2) maps to trace the velocity structures. Also, HCO⁺(3-2) blue profiles are seen toward the VeLLO candidate L328, indicating possible infall. To test theoretical models and to interpret the observations, we adopt a modeling sequence with self-consistent calculations of dust radiative transfer, gas energetics, chemistry, and line radiative transfer. In the L43 region described in Chapter 2, a starless core and a Class I protostar are evolving in the same environment. We modeled both sources with the same initial conditions to test the chemical characteristics with and without protostellar heating. The physical model consists of a series of Bonner-Ebert spheres describing the pre-protostellar (PPC) stages following by standard inside-out collapse (Shu 1977). The model best matches the observed lines suggests a longer total timescale at the PPC stage, with faster evolution at the later steps with higher densities. In Chapter 3, we modeled the entire group of Class 0 and I protostars. The trend of decreasing deuterium ratio can be seen after the temperature is high enough for CO to evaporate. After the evaporation, the history of heavy depletion (e.g, from longer PPC timescales or different grain surface properties) no longer affects the line intensities of gas-phase CO. The HCO⁺ blue profiles, which are used as infall indicators, are predicted to be observed when infall is beyond the CO evaporation front. The low luminosity of VeLLOs cannot be explained by standard models with steady accretion, and we tested an evolutionary model incorporating episodic accretion to investigate the thermal history and chemical behaviors. We tested a few chemical parameters to compare with the observations and the results from Chapter 2 and 3. The modeling results from episodic accretion models show that CO and N₂ evaporate from grain mantle surfaces at the accretion bursts and can freeze back onto grain surfaces during the long periods of quiescent phases. Deuterated species, such as N₂D⁺ and H₂D⁺, are most sensitive to the temperature. Possible good tracers for the thermal history include the line intensities of gas-phase N₂H+ relative to CO, as well as CO₂ and CO ice features. / text