The violent collision of asteroids and comets with solid planetary surfaces is a fundamental and ubiquitous process in the solar system. In the early history of our Solar System, small rocky particles collided and accreted to form larger and larger bodies until they grew into the planets we see today. For the Earth, the last of these planetary-scale collisions was a giant impact that ultimately formed the Moon. More recently in solar system history, a catastrophic impact event caused a mass extinction on Earth, including the demise of the dinosaurs. Today, the impact of an asteroid or comet poses a real, if poorly understood threat to humanity. Impact craters are also used to study the solar system. Counts of the number of impact craters on a solid planetary surface are used to distinguish older from younger terrains, and the shapes of large craters provide clues to the near-subsurface structure of a planet. The catastrophic potential of impact cratering, and its far-reaching consequences, make it imperative to understand exactly how the impact process works. Central to this are fundamental equations that relate the size of an impact crater to properties of the impacting object (for example, size and velocity) and conditions on the target body (for example, gravity). In other words, equations that give the answer to the fundamental question: how large will the crater be if a given impactor strikes a given target surface? At present we cannot adequately answer this question, because the equations do not properly include all the important impactor and target-material properties. The first aim of this proposal is to better constrain the relationship between all the important variables in an impact event using computer models. As these equations are fundamental tools for estimating the consequences of impact, this work will advance understanding in many areas of planetary science. The major missing pieces in these impact equations are an understanding of how the growth of the crater is affected by pore space in the target, and the angle at which the impactor strikes the target. The effect of impact angle is important to establish because well-studied vertical impacts are much less likely to occur than impacts at an angle greater than 30 degrees to the vertical, about which far less is known. Impact angle is observed to affect the size and shape of the crater in laboratory impacts, but quantifying the effect in larger impacts can only be established through numerical modelling. Porosity is an important property of asteroids, comets and the near-surface of most Solar System bodies. It is known from laboratory experiments that target rocks with a high porosity reduce the volume of material expelled from the crater during growth, but these effects have not yet been properly quantified. The effect of porous compaction during impact, in particular, may have important implications for the evolution of the solar system. Planets grow by the collision of planetesimals. Quantifying the transfer of energy and momentum in such collisions is therefore of vital importance for understanding the thermal, chemical and physical evolution of the solar system. In most previous work and models, collisions during planetary growth were assumed to be exclusively low-velocity and/or between non-porous planetesimals. However, recent work suggests that early planetesimals had very high porosities (up to 80%), and the growth of planetary embryos would have stirred relative velocities between planetesimals to >1 km/s. Experiments and our own modelling work show that target porosity dramatically affects the consequences of impact: increasing heating and reducing ejected mass. A second aim of this work is therefore to use numerical impact simulations to quantify the effect of planetesimal porosity on heating, compaction and ejection during early planetesimal collisions and assess the implications of this for solar system evolution.