Abstract. We offer an overview of the specification property, its relatives and their consequences. We examine relations between specification-like properties and such notions as: mixing, entropy, the structure of the simplex of invariant measures, and various types of the shadowing property. We pay special attention to these connections in the context of symbolic dynamics.The specification property is the ability to find a single point following ε-close an arbitrary collection of orbit segments, provided that the tracing point is allowed to spend a fixed (dependent on ε) time between consecutive segments.Rufus Bowen introduced the specification property in his seminal paper of 1971 on Axiom A diffeomorphisms [15]. In recent years this notion and its generalizations served as a basis for many developments in the theory of dynamical systems.This property is closely related to the study of hyperbolic systems initiated during the 1960's. Around that time Stephen Smale noticed that certain maps arising from forced oscillations and geodesic flows on surfaces of negative curvature had similar geometric and analytic properties. This motivated his definition of what we know today as uniformly hyperbolic systems. At the same time, the Russian school (an incomplete list contains such names as Anosov, Sinai, Katok) worked intensively on Anosov systems, that is, diffeomorphisms of manifolds under which the whole manifold is hyperbolic.Many properties of uniformly hyperbolic systems are consequences of the Specification Theorem [45, Thm. 18.3.9]. It states that a diffeomorphism restricted to a compact locally maximal hyperbolic set has the specification property. This result, together with the closely related Shadowing Theorem [45, Thm. 18.1.3] provides tools of great utility in exploring the topological structure and statistical behavior of uniformly hyperbolic systems. There are other important classes of dynamical systems that also have the specification property. Mixing interval maps or, more generally, graph maps, mixing cocyclic shifts (in particular, mixing sofic shifts, and thus shifts of finite type) are among them. Needless to say that this list, although impressive, does not contain all interesting systems. This motivates the search for other properties, call them specification-like, which may be used to examine systems without specification in Bowen's sense.In this survey we describe various notions designed to replace specification. It turns out that there are many systems lacking the specification property, but exhibiting a weaker version of it, which suffices to derive interesting results. This approach has been used to study systems with some forms of non-uniform hyperbolicity, such as β-shifts. Key words and phrases. specification property, almost specification property, weak specification property, approximate product property, topological mixing, shadowing, entropy, shift space, Poulsen simplex. The length of this paper does not allow detailed exposition of all aspects of the theory of specification-like p...