How do lambda (oxygen) sensors work and control engine air-fuel ratio?

Lambda sensors measure oxygen content in exhaust to determine air-fuel ratio. Narrowband sensors (zirconia or titania) provide binary output around stoichiometric (lambda=1.0). Wideband sensors provide linear output across the full range (0.7-1.3 lambda). The ECU uses sensor feedback in closed-loop to adjust fuel injection, maintaining stoichiometry for optimal three-way catalyst efficiency. Pre-catalyst sensors control mixture; post-catalyst sensors monitor catalyst function. Heated sensors enable rapid warm-up for emissions compliance.