Abstract: The Heisenberg limit (HL, with estimation error, scales as 1/n) and the standard quantum limit (SQL, 1/sqrt(n)) are two fundamental limits in estimating an unknown parameter in n copies of quantum channels and are achievable with full quantum controls, e.g., quantum error correction (QEC). It is unknown whether these limits are still achievable in restricted quantum devices when QEC is unavailable, e.g., with only unitary controls or bounded system sizes. In this talk, I will discuss various new limits for estimating qubit channels under restrictive controls. The HL is proven to be unachievable in various cases, indicating the necessity of QEC in achieving the HL. Furthermore, a necessary and sufficient condition to achieve the SQL is determined, where a novel unitary control protocol is identified to achieve the SQL for certain types of noisy channels, and a constant floor on the estimation error is proven for other cases.