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The recent discovery of intrinsic ferromagnetism in two-dimensional (2D) van der Waals crystals, such as CrI₃, has drawn much interest due to its potential for future 2D spintronic applications; however, the nature of the anisotropic magnetic interactions that allow 2D ferromagnetism and determine T_C in these materials remains poorly understood. In this work, we provide a detailed description of the anisotropic spin interactions in monolayer CrI₃ using a microscopic spin Hamiltonian constructed from the symmetries of the system. We present the results of our mean field theory and linear spin-wave theory calculations for this model and explain which interaction is responsible for stabilizing 2D ferromagnetic order in this system. Finally, we provide estimates for the strength of each interaction by comparing these results to our experimental data from angle-dependent ferromagnetic resonance on bulk CrI₃ single crystals.