This chapter explains the theoretical background necessary for understanding the translational motion of optically levitated nanoparticles. We first describe the fundamental mechanism of optical trapping using gradient forces. In particular, we focus on a one-dimensional optical lattice. This configuration enables strong confinement along the beam axis and supports higher trapping frequencies compared to single-beam traps. This chapter also provides the theoretical framework of the measurement of the nanoparticle’s position via detection of scattered light. We then introduce the power spectral density (PSD) of the position signal. We theoretically derive that the PSD area is related to the kinetic energy of particles. This forms the theoretical basis for evaluating phonon occupation numbers in later chapters. Finally, we present the theoretical limits of cold damping feedback cooling, accounting for noise from photon recoil and background gas collisions. This theoretical understanding is essential for the analysis of the experimental results presented in later chapters.