Bacteria, eukaryotic cells, multicellular organisms, animals, and even humans forage to find resources such as food. Foraging involves random search processes, and it has been shown that trajectories of many types of foragers resemble random walks. It is also known that solitary foragers can change their foraging strategy to maximize their encounter rate or search efficiency. While there has been much work done on foraging individually, less is known about foraging in groups. Members of a group can cooperate to find resources like herds of Mongolian gazelles, or compete with each other like tigers. The effect of cooperation and competition on foraging patterns is not yet fully understood. In this dissertation, we aim to increase our understanding by focusing on two specific cases - (i) efficient foraging strategies for territorial competitors and (ii) cooperative foraging in cell clusters. Many animals such as albatrosses are known to exhibit foraging patterns where the distances they travel in a given direction are drawn from a heavy-tailed Levy distribution. However, in nature, there also exist situations where multiple foragers interact with each other competitively. To understand the effects of competition, we develop a stochastic agent-based simulation that models competitive foraging among territorial individuals by incorporating a territory of a certain size around each forager which is not accessible by other competitors. While competition is common, many living organisms such as bees, school of fish, and caterpillars collaborate with each other to complete a task. Such collaboration extends to the cellular scale. Multicellular aggregates such as cell clusters and tissues exhibit collective migration with complex emergent behaviors that are critical for function and very different from the behavior of the constituent single cells. We focus on the chemotaxis of clusters of malignant lymphocytes, responsible for the metastases of lymphomas by using an agent-based model.