In this review paper we introduce currently available methods based on the Navier-Stokes equations for simulation of particulate flows which fully resolve the particles. The methods can be classified under two general categories based on the treatment of the underlying mesh namely fixed mesh methods and body-conformal mesh methods. We first consider body-conformal mesh methods and their properties. We then examine different steps of such algorithms and their application to many particle flow problems and argue why such implementations may not be feasible. Alternatively we discuss fixed mesh methods and categorize them into two subcategories namely immersed boundary methods and fictitious domain methods. A critical review of each method and their variations is provided bearing in mind the application to the particulate flow systems. The algorithms are covered in detail providing suggestions and guidelines for a successful implementation. Fundamental concepts such as discrete delta functions, body forces and calculation of surface integrals in fixed mesh methods are introduced in a simple and coherent way with simple examples and many illustrations. Major variations which are successfully applied to particulate flows are identified and the possibility of addition of heat transfer phenomena to the methods are discussed. (C) 2011 Elsevier Ltd. All rights reserved.