The phase portrait of a pendulum plots angular velocity (ω=dθ/dt) vs angle (θ), revealing the system's complete dynamics without solving for time. Fixed points appear as equilibria: the stable downward equilibrium (θ=0, ω=0) is a spiral sink when damped, while the unstable upward position (θ=π) is a saddle point. The separatrix — the curve passing through the saddle — divides librating orbits (oscillations) from rotating orbits (full rotations). Adding a periodic drive can create chaos (Poincaré sections become fractal) when the drive amplitude exceeds a critical threshold.