Memory is composed of several different abilities that are supported by different brain systems. The distinction between declarative (conscious) and nondeclarative (non-conscious) memory has proved useful in understanding the nature of eyeblink classical conditioning - the best understood example of classical conditioning in vertebrates. In delay conditioning, the standard procedure, conditioning depends on the cerebellum and brainstem and is intact in amnesia. Trace conditioning, a variant of the standard procedure, depends additionally on the hippocampus and neocortex and is impaired in amnesia. Recent studies have sharpened the contrast between delay and trace conditioning by exploring the importance of awareness. We discuss these new findings in relation to the brain systems supporting eyeblink conditioning and suggest why awareness is important for trace conditioning but not for delay conditioning.