In Europe, over recent years, there has been a marked shift in the regulatory approach to ensuring system safety. Whereas compliance with prescriptive safety codes and standards was previously the norm, the responsibility has now shifted back onto the developers and operators to construct and present well reasoned arguments that their systems achieve acceptable levels of safety. These arguments (together with supporting evidence) are typically referred to as a "safety case". This paper describes the role and purpose of a safety case (as defined by current safety and regulatory standards). Safety arguments within safety cases are often poorly communicated. This paper presents a technique called GSN (Goal Structuring Notation) that is increasingly being used in safety-critical industries to improve the structure, rigor, and clarity of safety arguments. Based upon the GSN approach, the paper also describes how an evolutionary and systematic approach to safety case construction, in step with system development, can be facilitated.