A wide range of information technology applications require the identification of a particular message or label that represents the identity of an object at a distance, e.g., over a wireless channel. Conventionally, the underlying information that represents the identity is transmitted over the channel, following the information-theoretic concept of message transmission. If the purpose of the interaction over the channel is only to verify (match) an identity, then the concept of identification over channels—utilizing the identification codes that have been developed by the information theory community—can provide an exponential efficiency gain over message transmission. This topical review article conducts for the first time a comprehensive detailed evaluation of the existing identification codes for the practically relevant regime of finite parameters. We examine essentially all published identification codes, including codes based on inner constant weight codes that are concatenated with outer linear block codes, such as Reed-Solomon and Reed-Muller codes. Specifically, we conduct a holistic identification code comparison based on the logarithm of the number of representable identities (in shannon), the size (in bit) of the transmitted cue that represents an identity, and the corresponding type II error probability bound for essentially all existing identification codes. Based on the resulting insights, we formulate guidelines for the design of practical (finite-parameter) identification codes. For instance, we find that a linear block code (without concatenation with a sophisticated inner constant-weight code) is sufficient for most practical identification code usages.