The group-contribution (GC) formalism for the description of the thermodynamic properties of fluids will be briefly reviewed with a particular emphasis on molecular approaches. The seminal contributions of John O'Connell in the area will be discussed with a particular emphasis on how formal statistical mechanics can be used to understand the fundamental assumptions which are implicit in GC methods. The recently developed predictive GC statistical associating fluid theory SAFT-γ will be described in some detail (A. Lymperiadis et al., J. Chem. Phys. 127, 234903, 2007). This approach represents an extension of the molecular-based SAFT-VR equation of state (A. Gil-Villegas et al., J. Chem. Phys. 106, 4168, 1997) to treat models of heteronuclear molecules formed from fused spherical segments of different types. This description is thus a heteronuclear generalization of the standard models used within SAFT, comparable to the optimized potentials for the liquid state OPLS models commonly used in molecular simulation; an advantage of our SAFT-&gamma approach over simulation is that an algebraic description for the thermodynamic properties of the model molecules can be developed. In our SAFT-γ treatment, each functional group in the molecule is modeled as different united-atom spherical square-well segments; more than one spherical segment can be used to represent large functional groups. The different groups are characterized by size (diameter), energy (well depth and range parameters representing the dispersive interaction), and by shape factor parameters which denote the extent to which each group contributes to the overall molecular geometry. For associating groups a number of bonding sites are included on the segment. In this case the site types, the number of sites of each type, and the appropriate association energy and range parameters also have to be specified. Our heteronuclear models are thus fundamentally different from those of the other GC-SAFT methods in which the GC concept is developed at the level of the parameters to give an average homonuclear chain molecule that can be treated within a standard SAFT platform. A number of chemical families including n-alkanes, branched alkanes, n-alkylbenzenes, mono- and di-unsaturated hydrocarbons, n-alkan-1-ols, n-alkan-1-amines, 2-ketones and n-carboxylic acids are examined in order to assess the quality of the SAFT-γ description of the vapor-liquid equilibria and to estimate the parameters of various functional groups. The group parameters for the functional groups present in these compounds CH₃, CH₂, CH₃CH, ACH, ACCH₂, CH₂=, CH=, OH, NH₂ , C=O, and COOH together with the unlike energy parameters between groups of different types are obtained from an optimal description of the pure component phase equilibria. The approach is found to describe accurately the vapor-liquid equilibria with an overall %AAD of 3.60% for the vapor pressure and 0.86% for the saturated liquid density. The fluid phase equilibria of some larger compounds comprising these groups, which are not included in the optimization database and some binary mixtures are examined to confirm the predictive capability of the SAFT-γ approach. A key advantage of our method is that the binary interaction parameters between groups can be estimated directly from an examination of pure components alone. This is particularly useful in describing the properties of fluid mixtures. The adequacy of the method in predicting the VLE is assessed for selected binary mixtures of associating and non-associating compounds. A strict test of any GC method is its ability to capture both vapor-liquid and liquid-liquid equilibria (LLE) with the same set of group parameters. It is very gratifying to find that with SAFT-γ one is able to reproduce simultaneously the VLE and LLE behavior behaviour for the mixtures tested to date, for example, n-hexane + propanone and n-pentane + polyethylene.