Excitatory and inhibitory (E & I) inputs to cortical neurons remain balanced across different conditions. The balanced network model provides a self-consistent account of this observation: population rates dynamically adjust to yield a state in which all neurons are active at biological levels, with their E & I inputs tightly balanced. But global tight E/I balance predicts population responses with linear stimulus-dependence and does not account for systematic cortical response nonlinearities such as divisive normalization, a canonical brain computation. However, when necessary connectivity conditions for global balance fail, states arise in which only a localized subset of neurons are active and have balanced inputs. We analytically show that in networks of neurons with different stimulus selectivities, the emergence of such localized balance states robustly leads to normalization, including sublinear integration and winner-take-all behavior. An alternative model that exhibits normalization is the Stabilized Supralinear Network (SSN), which predicts a regime of loose, rather than tight, E/I balance. However, an understanding of the causal relationship between E/I balance and normalization in SSN and conditions under which SSN yields significant sublinear integration are lacking. For weak inputs, SSN integrates inputs supralinearly, while for very strong inputs it approaches a regime of tight balance. We show that when this latter regime is globally balanced, SSN cannot exhibit strong normalization for any input strength; thus, in SSN too, significant normalization requires localized balance. In summary, we causally and quantitatively connect a fundamental feature of cortical dynamics with a canonical brain computation. Time allowing I will also cover our work extending a normative theoretical account of normalization which explains it as an example of efficient coding of natural stimuli. We show that when biological noise is accounted for, this theory makes the same prediction as the SSN: a transition to supralinear integration for weak stimuli.