The Vicsek model (1995): N self-propelled particles at speed v update their heading toward the average of neighbors within radius r, plus noise η. The order parameter φ = |⟨e^{iθ}⟩| measures collective alignment. At low noise/high density: φ→1 (flock). The transition is discontinuous (first-order) despite looking continuous in finite systems — a landmark result challenging Mermin-Wagner for active matter. Giant number fluctuations ΔN ~ N^α with α>0.5 distinguish the flocking phase from equilibrium.