Empathy indicates an individual's ability to understand others. Over the past few years, empathy has drawn attention from various disciplines, including but not limited to Affective Computing, Cognitive Science, and Psychology. Detecting empathy has potential applications in society, healthcare and education. Despite being a broad and overlapping topic, the avenue of empathy detection leveraging Machine Learning remains underexplored from a systematic literature review perspective. We collected 849 papers from 10 well-known academic databases, systematically screened them and analysed the final 82 papers. Our analyses reveal several prominent task formulations - including empathy on localised utterances or overall expressions, unidirectional or parallel empathy, and emotional contagion - in monadic, dyadic and group interactions. Empathy detection methods are summarised based on four input modalities - text, audiovisual, audio and physiological signals - thereby presenting modality-specific network architecture design protocols. We discuss challenges, research gaps and potential applications in the Affective Computing-based empathy domain, which can facilitate new avenues of exploration. We further enlist the public availability of datasets and codes. This paper, therefore, provides a structured overview of recent advancements and remaining challenges towards developing a robust empathy detection system that could meaningfully contribute to enhancing human well-being.