Precision livestock farming (PLF) aims to improve the health and welfare of livestock animals and farming outcomes through the use of advanced technologies. Computer vision, combined with recent advances in machine learning and deep learning artificial intelligence approaches, offers a possible solution to the PLF ideal of 24/7 livestock monitoring that helps facilitate early detection of animal health and welfare issues. However, a significant number of livestock species are raised in large outdoor habitats that pose technological challenges for computer vision approaches. This review provides a comprehensive overview of computer vision methods and open challenges in outdoor animal monitoring. We include research from both the livestock and wildlife fields in the review because of the similarities in appearance, behaviour, and habitat for many livestock and wildlife. We focus on large terrestrial mammals, such as cattle, horses, deer, goats, sheep, koalas, giraffes, and elephants. We use an image processing pipeline to frame our discussion and highlight the current capabilities and open technical challenges at each stage of the pipeline. The review found a clear trend towards the use of deep learning approaches for animal detection, counting, and multi-species classification. We discuss in detail the applicability of current vision-based methods to PLF contexts and promising directions for future research.