Western boundary currents are ocean currents that transport large masses of water, usually poleward from the equator. Therefore, they contribute to heat redistribution at a global scale, and are essential to understanding the Earth's climate. These currents are boundary layers, and are generally smaller than the mesh size of the models used to predict future climates (at low resolution). Their numerical representation and physical understanding are therefore necessary when attempting to predict climate changes. This presentation will briefly introduce western boundary currents, then we will see how such boundary layers naturally appear from a simple 2D toy-model introduced in the '50s, and finally introduce a toy model derived from the Boussinesq equations that shows the interaction between a western boundary current and a topographic slope, a key physical phenomenon for understanding the detachment of these currents along the coast.