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The literature on bargaining problems dating back to John Nash's (1950) seminal piece takes an axiomatic perspective. Intuitive, desirable properties that solutions to bargaining problems should satisfy are formalized and represented as axioms. Different solution concepts that capture various real-life bargaining scenarios are introduced and these solution concepts are characterized using normative properties (i.e., axioms). In this talk, we will formally introduce the bargaining problem, the axiomatic approach, two of the most well-known solution concepts (Nash solution and Kalai-Smorodinsky solution) along with the axioms that characterize them.