This dissertation aims to provide better understanding of volcanism and impacts on Mars and the Moon through the use of topographic and petrologic analyses. Chapter 2 examines the topographic characteristics of polar volcanic edifices in the Borealis Volcanic Field of Mars and, through the use of Icelandic analogs, suggests the existence of a former ice sheet. Chapter 3 examines the depth-diameter relationship, cavity wall slopes, and morphologic characteristics of interior topographic formations within Martian North polar impact craters to constrain polar processes and possible target effects. Changing celestial spheres, chapter 4 is a detailed explanation of the geochemical methods of analysis employed for the Lunar petrology studies in chapters 5-7; these chapters focus on the petrology of basalt and impact melt samples from Apollo 14 and 16 missions. First, in chapter 5, the composition and textural characteristics of olivine crystals are used to distinguish between Apollo 14 impact melt-generated olivine vitrophyres and pristine mare basalts of similar texture in a minimally destructive method. Next, in chapter 6 whole-rock composition and chemistry of mineral phases are employed to examine rare basalt clasts from Apollo 16 and suggest a common component to highly evolved Apollo 17 Type A Basalts. The final chapter focuses on the chemistry of atypical plagioclase crystals with negative Eu anomalies and the bulk composition of the samples therein to suggest the incorporation of a KREEP component into an impact melt to account for the anomaly. This work highlights the vast knowledge than can be gained about these two processes both remotely and with small sample aliquots.