The availability of feedback from the receiver to the transmitter in a communication system can play a significant role. In this dissertation, our focus is specifically on binary or one-bit feedback. First, we study the problem of successive beam alignment for millimeter-wave channels where the receiver sends back only one-bit of information per beam sounding. The sparse nature of the channel allows us to interpret channel sounding as a form of questioning. By posing the alignment problem as a questioning strategy, we describe adaptive (closed-loop) and non-adaptive (open-loop) channel sounding techniques which are robust to erroneous feedback signals caused by noisy quantization. In the second part, we tightly characterize the capacity for two binary stochastic-adversarial mixed noise channels. Specifically, the transmitter (Alice) intends to convey a message to the receiver (Bob) over a binary symmetric channel (BSC) or a binary erasure channel (BEC) in the presence of an adversary (Calvin) who injects additional noise at the channel's input subject to a budget constraint. Calvin is online or causal in that at any point during the transmission, he can infer the bits being sent by Alice and those being received by Bob via a feedback link. Finally in the third part, we study the applicability of binary feedback for encoding and propose the framework of linearly adapting block feedback codes. We also prove a new result for Reed-Muller (RM) codes to demonstrate how an uncoded system can mimic a RM code under this framework, against remarkably large feedback delays.