In the past few years, osmotic membrane systems, such as forward osmosis (FO), have gained popularity as “soft” concentration processes. FO has unique properties by combining high rejection rate and low fouling propensity and can be operated without significant pressure or temperature gradient, and therefore can be considered as a potential candidate for a broad range of concentration applications where current technologies still suffer from critical limitations. This review extensively compiles and critically assesses recent considerations of FO as a concentration process for applications, including food and beverages, organics value added compounds, water reuse and nutrients recovery, treatment of waste streams and brine management. Specific requirements for the concentration process regarding the evaluation of concentration factor, modules and design and process operation, draw selection and fouling aspects are also described. Encouraging potential is demonstrated to concentrate streams more than 20-fold with high rejection rate of most compounds and preservation of added value products. For applications dealing with highly concentrated or complex streams, FO still features lower propensity to fouling compared to other membranes technologies along with good versatility and robustness. However, further assessments on lab and pilot scales are expected to better define the achievable concentration factor, rejection and effective concentration of valuable compounds and to clearly demonstrate process limitations (such as fouling or clogging) when reaching high concentration rate. Another important consideration is the draw solution selection and its recovery that should be in line with application needs (i.e., food compatible draw for food and beverage applications, high osmotic pressure for brine management, etc.) and be economically competitive.