The COVID-19 pandemic that began in 2019 has resulted in millions of deaths worldwide. Over this period, the economic and healthcare consequences of COVID-19 infection in survivors of acute COVID-19 infection have become apparent. During the course of the pandemic, computer analysis of medical images and data have been widely used by the medical research community. In particular, deep-learning methods, which are artificial intelligence (AI)-based approaches, have been frequently employed. This paper provides a review of deep-learning-based AI techniques for COVID-19 diagnosis using chest radiography and computed tomography. Thirty papers published from February 2020 to March 2022 that used two-dimensional (2D)/three-dimensional (3D) deep convolutional neural networks combined with transfer learning for COVID-19 detection were reviewed. The review describes how deep-learning methods detect COVID-19, and several limitations of the proposed methods are highlighted.