\textbf{Context:} Empathy is increasingly recognized as a critical human capability for software engineers, supporting collaboration, ethical awareness, and user-centered design. While many disciplines have long explored empathy as part of professional formation, its incorporation into software engineering education remains fragmented. \textbf{Aim:} This study investigates how empathy has been used, taught, and discussed in general engineering and software engineering education, with the goal of identifying pedagogical practices, outcomes, and disciplinary differences that inform the structured integration of empathy into software curricula. \textbf{Method:} Following established guidelines for systematic reviews in software engineering, we conducted a comprehensive search across six databases and analyzed 43 primary studies published between 2001 and 2025. Data were coded and synthesized using descriptive and thematic analysis to capture how empathy is conceptualized, fostered, and assessed across educational contexts. \textbf{Findings:} Our findings show that engineering programs frame empathy as an ethical and reflective capacity linked to social responsibility, whereas software engineering translates empathy into structured, design-oriented, and measurable practices. Across both domains, empathy teaching enhances collaboration, ethical reasoning, bias awareness, and motivation, but remains limited by low curricular prioritization, measurement challenges, and resource constraints. \textbf{Conclusion:} Empathy is evolving from a peripheral soft skill into a measurable pedagogical construct in software engineering education. Embedding empathy as a continuous, assessable component of design and development courses can strengthen inclusivity, ethical reflection, and responsible innovation in future software professionals.