Yield curves are typically built from a limited set of observable bonds (e.g., 2Y, 5Y, 10Y, 30Y Treasuries), but you often need yields at intermediate maturities — say, 7 years — that don't have a liquid benchmark. Curve interpolation fills these gaps. Linear interpolation is the simplest method: draw a straight line between the two nearest points. For example, if 5Y yields 3.0% and 10Y yields 3.5%, linear interpolation estimates 7Y at 3.3%. This keeps the curve smooth without making complex shape assumptions. More sophisticated methods (cubic splines, Nelson-Siegel) produce smoother curves and are used when precision matters for derivatives pricing or portfolio analytics.