Capsule endoscopy (CE) is a widely used medical imaging tool for the diagnosis of gastrointestinal tract abnormalities like bleeding. However, CE captures a huge number of image frames, constituting a time-consuming and tedious task for medical experts to manually inspect. To address this issue, researchers have focused on computer-aided bleeding detection systems to automatically identify bleeding in real time. This paper presents a systematic review of the available state-of-the-art computer-aided bleeding detection algorithms for capsule endoscopy. The review was carried out by searching five different repositories (Scopus, PubMed, IEEE Xplore, ACM Digital Library, and ScienceDirect) for all original publications on computer-aided bleeding detection published between 2001 and 2023. The Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA) methodology was used to perform the review, and 147 full texts of scientific papers were reviewed. The contributions of this paper are: (I) a taxonomy for computer-aided bleeding detection algorithms for capsule endoscopy is identified; (II) the available state-of-the-art computer-aided bleeding detection algorithms, including various color spaces (RGB, HSV, etc.), feature extraction techniques, and classifiers, are discussed; and (III) the most effective algorithms for practical use are identified. Finally, the paper is concluded by providing future direction for computer-aided bleeding detection research.