We consider the problems of online decision making under two categories of information-theoretical constraints, namely, security and communication constraints. There are several security related performance metrics that are considered in this thesis. When the decision maker aims to avoid the adversary from gaining accurate estimation about the unknown parameter, we formulate the problem of evasive hypothesis testing. This problem can be viewed as the counterpart of  secured communication in the context of hypothesis testing. The objective is to maximize the quantity which captures the ratio of error exponents between the decision maker and the adversary. When the goal is not to hide the parameter but to make the process of decision making algorithm undetectable, we formulate the problem of  covert decision making. We show the algorithm also need to obey the square-root law in order to hide the presence of the algorithm. The last security related performance metric we consider in this thesis is the robustness of the algorithm. We are interested in analyzing the performance of active hypothesis testing when actions are potentially corrupted by the adversary. 
Problems that involve jointly estimating the channel state and transmitting information are called joint communication and sensing. In the second half of this thesis, we analyze the tradeoff between the detection error exponent and the communication rate in the problems of joint communication and sensing in both mono-static and bi-static models.
Finally, we also make an extension to the case when the transmission window can be determined online, and we call it sequential joint communication and sensing.