As Artificial Intelligence (AI) systems become more widespread, there is a growing need for transparency to ensure human understanding and oversight. This is where Explainable AI (XAI) comes in to make AI systems more transparent and interpretable. However, developing adequate explanations is still an open research problem. Human-Computer Interaction (HCI) is significant in designing interfaces for explainable AI. This article reviews the HCI techniques that can be used for solvable AI systems. The literature was explored with a focus on papers at the intersection of HCI and XAI. Essential techniques include interactive visualizations, natural language explanations, conversational agents, mixed-initiative systems, and model introspection methods while Explainable AI presents opportunities to improve system transparency, it also comes with risks, especially if the explanations need to be designed carefully. To ensure that explanations are tailored for diverse users, contexts, and AI applications, HCI principles and participatory design approaches can be utilized. Therefore, this article concludes with recommendations for developing human-centred XAI systems, which can be achieved through interdisciplinary collaboration between HCI and AI. As Artificial Intelligence (AI) systems become more common in our daily lives, the need for transparency in these systems is becoming increasingly important. Ensuring that humans clearly understand how AI systems work and can oversee their functioning is crucial. This is where the concept of Explainable AI (XAI) comes in to make AI systems more transparent and interpretable. However, developing adequate explanations for AI systems is still an open research problem. In this context, Human-Computer Interaction (HCI) is significant in designing interfaces for explainable AI. By integrating HCI principles, we can create systems humans understand and operate more efficiently. This article reviews the HCI techniques that can be used for solvable AI systems. The literature was explored with a focus on papers at the intersection of HCI and XAI. The essential methods identified include interactive visualizations, natural language explanations, conversational agents, mixed-initiative systems, and model introspection methods. Each of these techniques has unique advantages and can be used to provide explanations for different types of AI systems. While Explainable AI presents opportunities to improve system transparency, it also comes with risks, especially if the explanations need to be designed carefully. There is a risk of oversimplification, leading to misunderstanding or mistrust of the AI system. It is essential to employ HCI principles and participatory design approaches to ensure that explanations are tailored for diverse users, contexts, and AI applications. By developing human-centred XAI systems, we can ensure that AI systems are transparent, interpretable, and trustworthy. This can be achieved through interdisciplinary collaboration between HCI and AI. The recommendations in this article provide a starting point for designing such systems. In essence, XAI presents a significant opportunity to improve the transparency of AI systems, but it requires careful design and implementation to be effective.