In the field of biomedical imaging, ultrasonography has become increasingly widespread, and an important auxiliary diagnostic tool with unique advantages, such as being non-ionising and often portable . This article reviews the state-of-the-art in medical ultrasound image computing and in particular its application in the examination of the lungs . First, we review the current developments in medical ultrasound technology . We then focus on the characteristics of lung ultrasonography and on its ability to diagnose a variety of diseases through the identification of various artefacts . We review medical ultrasound image processing methods by splitting them into two categories: (1) traditional model-based methods, and (2) data driven methods . For the former, we consider inverse problem based methods by focusing in particular on ultrasound image despeckling, deconvolution, and line artefacts detection . Among the data-driven approaches, we discuss various works based on deep/machine learning, which include various effective network architectures implementing supervised, weakly supervised and unsupervised learning.