Automatic speech recognition (ASR) models are central to voice-driven AI applications, enabling transcription, speaker diarization, intent recognition, and other downstream tasks. Recent advances in deep learning and large-scale foundation models have significantly improved ASR accuracy, making high-performance ASR models widely accessible through open-source frameworks and commercial application programming interfaces (APIs). However, there remains a lack of comprehensive surveys examining the capabilities, architectures, and deployment mechanisms of these APIs. This paper provides a systematic review of ASR APIs, categorizing them into open-source libraries, cloud-based services, and commercial offerings. We analyze the strengths and limitations of prevalent ASR architectures, including Connectionist Temporal Classification, Sequence-to-Sequence, and transducer-based models, and discuss key API features such as multilingual transcription, real-time processing, and customization. Additionally, we highlight critical challenges in ASR, including evaluation metric limitations, low-resource language modeling, and transcription accuracy disparities for individuals with speech differences. By presenting a structured overview of ASR APIs and their challenges, this work aims to support researchers, developers, and practitioners in selecting and deploying ASR technologies effectively. Addressing existing ASR challenges will be crucial to ensuring more inclusive, robust, and accessible voice AI applications.