Cognitive radios, as sensing-capable agents, are able to monitor the dynamics of the spectral activity in wireless networks. The sensed information can be collectively processed in order to identify the segments of the spectrum under-utilized by the legacy (primary) users. The cognitive (secondary) users can benefit from this fact and opportunistically access such under-utilized spectrum segments (spectrum holes). Due to the transient and rapidly-varying nature of the spectrum occupancy, the secondary users must be agile in identifying the spectrum holes to enhance their spectral efficiency. We propose a novel sequential  and adaptive procedure to reinforce the agility of the secondary users. This is accomplished by successively refining the set of potential spectrum holes and progressively allocating the sensing resources to the most promising areas of the spectrum. Such refinement and resource allocation results in conservative spending of the sensing resources and translates into very agile spectrum monitoring. Such sequential and adaptive sensing is in contrast with the more conventional approaches that allocate the sampling budget equally over the entire spectrum. Besides improved agility, the adaptive procedure requires less-stringent constraint on the power of the primary users to guarantee they remain distinguishable from the environment noise. This renders more reliable spectrum hole detection as well.