As we rely more and more on computer software for automating processes and making decisions, the range of software that is considered critical goes well beyond the avionics and nuclear power industries: nowadays software plays an increasingly important role in convicting criminals, trading on the financial markets, autonomously driving cars, and performing medical diagnoses, to name a few applications. It is now paramount to ensure the reliability and security of such software, and expectations about software fairness and transparency are rapidly rising. To meet these needs, we need new mathematical models of software behavior that capture the aspects relevant for a particular dependability property, and new algorithmic approaches to effectively navigate this mathematical space and decide whether the software behaves as desired. This talk gives an overview of the steps I have taken towards addressing these challenges. Starting from a series of works on deciding software termination, I show that the insights from this domain are transferable to other formal methods and properties. These results pave the way for a unified framework for deciding increasingly advanced software dependability properties. I discuss the first results that I obtained in this more general direction, which in particular bring new conceptual clarity to the synergies with deciding security properties of software. Finally, I conclude with an outlook to the future and discuss the potential impact of this research on our personal, civic, and economic life.