Computational methods have increased the objectivity of measures of human behavior and positioned personality science to benefit from the ongoing digital revolution. In this review, we define and discuss computational personality assessment (CPA), a measurement process that uses computational technologies to obtain estimates of personality. We briefly review some of the most promising sources of data currently used for CPA: mobile sensing, digital footprints from social media, images, language, and experience sampling. We present a concise overview of key findings, discuss the promise and opportunities of CPA (e.g., moving towards objective measures of personality, obtaining new insights from big data), and highlight important limitations and challenges in the development and application of CPA (e.g., establishing reliability and validity, selecting appropriate ground truth criterion, assessing affect and cognition, implications for ethics and privacy). We conclude with our perspective on how CPA could change our understanding of individual differences.