An emerging subject in nonequilibrium physics is “order parameter steering” where experimentally controllable perturbations (e.g., light pulses) may drive the order parameters of symmetry broken phases to evolve in time. I will theoretically demonstrate this phenomenon in two cases: mean field steering and fluctuation steering. In the first case, we show that in excitonic insulators with s-wave electron-hole pairing, an applied light pulse can induce a p-wave component to the order parameter, and further drive it to rotate in the s+ip plane. In one dimension, each cycle of rotation pumps exactly two electrons across the sample while higher dimensional systems are similar, realizing a Thouless charge pump as a collective manybody effect. In the second case, we study the dynamics of a competing order system which is rapidly heated up by a pump and then cools down. In the cooling process, exponentially growing thermal fluctuations lead the system into the phase associated with the faster-relaxing order parameter, which is not necessarily the ground state. This theory offers a natural explanation for the widespread experimental observation that metastable states may be induced by laser pulses. References: PRL 126, 027601 (2021), PRX 10, 021028 (2020)