Cells are equipped with asymmetrically localised and functionally specialised components, including cytoskeletal structures and organelles. Positioning these components to specific intracellular locations in an asymmetric manner is critical for their functionality and affects processes like immune responses, tissue maintenance, muscle functionality, and neurobiology. Here, we provide an overview of strategies to actively move, position, and anchor organelles to specific locations. By conceptualizing the cytoskeletal forces and the organelle-to-cytoskeleton connectivity, we present a framework of active positioning of both membrane-enclosed and membrane-less organelles. Using this framework, we discuss how different principles of force generation and organelle anchorage are utilised by different cells, such as mesenchymal and amoeboid cells, and how the microenvironment influences the plasticity of organelle positioning. Given that motile cells face the challenge of coordinating the positioning of their content with cellular motion, we particularly focus on principles of organelle positioning during migration. In this context, we discuss novel findings on organelle positioning by anchorage-independent mechanisms and their advantages and disadvantages in motile as well as stationary cells.