This paper explores the concept of counterfactual explanations as a means to provide explanations for automated decisions without opening the "black box" of algorithmic decision-making systems. The authors argue that counterfactual explanations can serve three key purposes: (1) to help data subjects understand why a particular decision was made, (2) to provide grounds for contesting adverse decisions, and (3) to guide data subjects on how to change their behavior or circumstances to achieve a desired outcome in the future. These explanations do not require revealing the internal logic of the decision-making system, which is a key distinction from traditional explanations that aim to convey the internal workings of algorithms. The authors examine the implications of counterfactual explanations for the GDPR, which includes provisions for the "right to explanation" in automated decision-making. While the GDPR does not legally bind data subjects to receive explanations, it does require that data subjects be informed about the nature and purpose of automated decision-making, including the existence of profiling and the significance and consequences of such processing. The authors argue that counterfactual explanations can align with these requirements by providing data subjects with information that is both easily digestible and practically useful for understanding the rationale behind decisions, challenging them, and altering future behavior. Counterfactual explanations are defined as statements that describe how the world would have to be different for a desirable outcome to occur. They are generated by altering variables in a decision-making system to achieve a different outcome, while keeping other variables constant. The authors demonstrate that counterfactual explanations can be generated using various distance functions, including the L1 norm and the L2 norm, and that they can be applied to a wide range of datasets, including the LSAT dataset and the Pima Diabetes Database. The authors also discuss the advantages of counterfactual explanations over traditional explanations, which often require revealing the internal logic of algorithms. Counterfactual explanations are more practical for data subjects, as they provide information that is both easily understood and actionable. They also do not require data controllers to disclose the internal workings of their algorithms, which can be a significant concern for privacy and trade secrets. The paper concludes that counterfactual explanations can serve as a valuable tool for meeting the requirements of the GDPR, particularly in terms of providing data subjects with information that is both meaningful and actionable. The authors argue that counterfactual explanations can help bridge the gap between the interests of data subjects and data controllers, which is a key challenge in the implementation of the GDPR.This paper explores the concept of counterfactual explanations as a means to provide explanations for automated decisions without opening the "black box" of algorithmic decision-making systems. The authors argue that counterfactual explanations can serve three key purposes: (1) to help data subjects understand why a particular decision was made, (2) to provide grounds for contesting adverse decisions, and (3) to guide data subjects on how to change their behavior or circumstances to achieve a desired outcome in the future. These explanations do not require revealing the internal logic of the decision-making system, which is a key distinction from traditional explanations that aim to convey the internal workings of algorithms. The authors examine the implications of counterfactual explanations for the GDPR, which includes provisions for the "right to explanation" in automated decision-making. While the GDPR does not legally bind data subjects to receive explanations, it does require that data subjects be informed about the nature and purpose of automated decision-making, including the existence of profiling and the significance and consequences of such processing. The authors argue that counterfactual explanations can align with these requirements by providing data subjects with information that is both easily digestible and practically useful for understanding the rationale behind decisions, challenging them, and altering future behavior. Counterfactual explanations are defined as statements that describe how the world would have to be different for a desirable outcome to occur. They are generated by altering variables in a decision-making system to achieve a different outcome, while keeping other variables constant. The authors demonstrate that counterfactual explanations can be generated using various distance functions, including the L1 norm and the L2 norm, and that they can be applied to a wide range of datasets, including the LSAT dataset and the Pima Diabetes Database. The authors also discuss the advantages of counterfactual explanations over traditional explanations, which often require revealing the internal logic of algorithms. Counterfactual explanations are more practical for data subjects, as they provide information that is both easily understood and actionable. They also do not require data controllers to disclose the internal workings of their algorithms, which can be a significant concern for privacy and trade secrets. The paper concludes that counterfactual explanations can serve as a valuable tool for meeting the requirements of the GDPR, particularly in terms of providing data subjects with information that is both meaningful and actionable. The authors argue that counterfactual explanations can help bridge the gap between the interests of data subjects and data controllers, which is a key challenge in the implementation of the GDPR.