This chapter is interested in the epistemology of algorithms. As I intend to approach the topic, this is an issue about epistemic justification. Current approaches to justification emphasize the transparency of algorithms, which entails elucidating their internal mechanisms -- such as functions and variables -- and demonstrating how (or that) these produce outputs. Thus, the mode of justification through transparency is contingent on what can be shown about the algorithm and, in this sense, is internal to the algorithm. In contrast, I advocate for an externalist epistemology of algorithms that I term computational reliabilism (CR). While I have previously introduced and examined CR in the field of computer simulations ([42, 53, 4]), this chapter extends this reliabilist epistemology to encompass a broader spectrum of algorithms utilized in various scientific disciplines, with a particular emphasis on machine learning applications. At its core, CR posits that an algorithm's output is justified if it is produced by a reliable algorithm. A reliable algorithm is one that has been specified, coded, used, and maintained utilizing reliability indicators. These reliability indicators stem from formal methods, algorithmic metrics, expert competencies, cultures of research, and other scientific endeavors. The primary aim of this chapter is to delineate the foundations of CR, explicate its operational mechanisms, and outline its potential as an externalist epistemology of algorithms.