We present a model of soft active particles that leads to a rich array of collective behavior found also in dense biological swarms of bacteria and other unicellular organisms. Our model uses only local interactions, such as Vicsek-type nearest neighbor alignment, short-range repulsion, and a local boundary term. Changing the relative strength of these interactions leads to migrating swarms, rotating swarms and jammed swarms, as well as swarms that exhibit run-and-tumble motion, alternating

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... een migration and either rotating or jammed states. Interestingly, although a migrating swarm moves slower than an individual particle, the diffusion constant can be up to three orders of magnitude larger, suggesting that collective motion can be highly advantageous, for example, when searching for food.