Diffusion MRI (dMRI) has become a crucial imaging technique within the field of neuroscience and has an increasing number of clinical applications. Although most studies still focus on the brain, there is a growing interest in utilizing dMRI to investigate the healthy or injured spinal cord. The past decade has also seen the development of biophysical models that link MR-based diffusion measures to underlying microscopic tissue characteristics. Building upon 13 years of research and development, we present an open-source, MATLAB-based academic software toolkit dubbed ACID: A Comprehensive Toolbox for Image Processing and Modeling of Brain, Spinal Cord, and Post-mortem Diffusion MRI Data. ACID is designed to process and model dMRI data of the brain, spinal cord, and post-mortem specimens by incorporating state-of-the-art artifact correction tools, diffusion and kurtosis tensor imaging, and biophysical models that enable the estimation of microstructural properties in white matter. Additionally, the software includes an array of linear and non-linear fitting algorithms for accurate diffusion parameter estimation. By adhering to the Brain Imaging Data Structure (BIDS) data organization principles, ACID facilitates standardized analysis, ensures compatibility with other BIDS-compliant software, and aligns with the growing availability of large databases utilizing the BIDS format. Furthermore, ACID seamlessly integrates into the popular Statistical Parametric Mapping (SPM) framework, benefitting from a wide range of established segmentation, spatial processing, and statistical analysis tools as well as a large and growing number of SPM extensions. As such, this comprehensive toolbox covers the entire processing chain from raw DICOM data to group-level statistics, all within a single software package.