Trust, privacy, and interpretability have emerged as significant concerns for experts deploying deep learning models for security monitoring. Due to their back-box nature, these models cannot provide an intuitive understanding of the machine learning predictions, which are crucial in several decision-making applications, like anomaly detection. Security operations centers have a number of security monitoring tools that analyze logs and generate threat alerts which security analysts inspect. The alerts lack sufficient explanation on why it was raised or the context in which they occurred. Existing explanation methods for security also suffer from low fidelity and low stability and ignore privacy concerns. However, explanations are highly desirable; therefore, we systematize this knowledge on explanation models so they can ensure trust and privacy in security monitoring. Through our collaborative study of security operation centers, security monitoring tools, and explanation techniques, we discuss the strengths of existing methods and concerns vis-a-vis applications, such as security log analysis. We present a pipeline to design interpretable and privacy-preserving system monitoring tools. Additionally, we define and propose quantitative metrics to evaluate methods in explainable security. Finally, we discuss challenges and enlist exciting research directions for explorations.