Tribology is the science and technology of interacting surfaces in relative motion and of related subjects and practices. The nature and consequences of the interactions that take place at the moving interface control its friction, wear, and lubrication behavior. Understanding the nature of these interactions and solving the technological problems associated with the interfacial phenomena constitute the essence of tribology. The field of tribology incorporates a number of disciplines, including mechanical engineering, materials science, mechanics, surface chemistry, surface physics and a multitude of subjects, such as surface characterization, friction, wear, lubrication, bearing materials, lubricants, and the selection and design of lubrication systems, and it forms a vital element of engineering. The importance of friction and wear control cannot be overemphasized for economic reasons and long-term reliability. It is important that all designers of mechanical systems use appropriate means to reduce friction and wear, through the proper selection of bearings and the selection of appropriate lubricants and materials for all interacting surfaces. It is equally important that those involved with manufacturing understand the tribological origins of unwanted friction, excessive wear, and lubrication failure in their equipment. The lack of consideration of tribological fundamentals in design and manufacturing is responsible for vast economic losses, including shortened life, excessive equipment downtime, and large expenditures of energy. The recent emergence and proliferation of proximal probes (in particular tip-based microscopies and the surface force apparatus) and of computational techniques for simulating tip-surface interactions and interfacial properties has allowed systematic investigations of interfacial problems with high resolution as well as ways and means for modifying and manipulating nanostructures. These advances provide the impetus for research aimed at developing a fundamental understanding of the nature and consequences of the interactions between materials on the atomic scale, and they guide the rational design of material for technological applications. In short, they have led to the appearance of the new field of micro/Nano tribology. There are also new applications which require detailed understanding of the tribological processes on macro- and micro scales. Since the early 1980s, tribology of magnetic storage systems has become one of the important parts of tribology. Microelectromechanical Systems (MEMS) have begun to appear in the marketplace which present new tribological challenges. Tribology of processing systems such as copiers, printers, scanners, and cameras is important, although it has not received much attention. Along with the new industrial applications, there has been development of new materials, coatings, and treatments, such as synthetic diamond, true diamond, diamond-like carbon films, and chemically grafted films, to name a few. It is clear that the general field of tribology has grown rapidly during the past 50 years. Conventional tribology is well established, but micro/Nano tribology is evolving and is expected to take center stage for the next decade. New materials are needed, and their development requires fundamental understanding of tribological processes. Furthermore, new industrial applications continue to evolve with their unique challenges. Much of the new tribological information has not made it into the hands. The tribology deals with rough surface contact and accordingly numerical methods for such surface are strongly needed to evaluate such situations as follows:- An alternative numerical method for solving contact problems for real rough surfaces is proposed in all tribological problems. The real area of contact and the contact pressure distribution are determined using a single-loop iteration scheme based on the conjugate gradient method, which converges for arbitrary rough surfaces. The surface deflections and subsurface stresses are computed using an alternative two-dimensional multi-level multi-summation algorithm, which allows the summation error to be kept under the discretization error for any number of contact points. The most interested area in tribology field is the biomedical tribology, however With recent advancements in medical science, there have been improvements in the quality of human life. The discoveries in the field of materials has positively impacted the development of prosthetics and implants, which are becoming more biocompatible as well as durable. To gain knowledge of the tribological characteristics of these materials, namely friction, wear, and corrosion, is significant in order to further enhance their durability, leading to a decrease in the frequency of surgical replacement and a more normal life for the patient. Hence, this chapter explores the tribological implications of various materials employed in biomedical applications which is include the followings:-  Tribology of natural synovial joints and artificial replacements.  Wear of dental implants.  Wear and replacement of heart valves.  Lubrication of pump in total artificial hearts.  Ocular tribology and tribology of contact lenses. The following figure illustrated apart of biomedical tribology material and elements. So, the biomaterials science and engineering has progressed quickly over the past decades, the development of this field has shifted to the design of new materials and devices wherein the functionality, reliability, and biocompatibility have become more specific and significant. Tribology-related behavior is one of the key points for the above aspects. For instance, The major clinical problem associated with artificial joints is excessive wear and loosening, which can be attributed to their poor tribological properties and thus generated wear debris. In addition, narrowing or blockage of artificial vascular due to surface coagulation and damage to artificial heart valves owing to fatigue wear are also examples of the failure of biomaterials and medical devices in tribology. Therefore, to assure the functionality, reliability, and biocompatibility of biomaterials, especially for long-term implanted medical devices, studying various tribological damage mechanisms and obtaining optimum properties is one of the most important goals. Driven by this point, more and more investigations have been conducted on fundamental theories, bionic design, damage palliative related to tribology in biomedical applications. Progress has been achieved, but problems remain to be answered. This is a challenging but attractive task. another advanced and interest area in tribology is the Nano tribology which is the scientific study of friction and wear on the nanometer length scale, typically addressing the sliding contact between a single asperity and a flat surface in well-controlled conditions through experiments, modeling, and atomistic simulations. The micro/Nano-tribological studies are needed to develop fundamental understanding of interfacial phenomena on a small scale and to study interfacial phenomena involving ultrathin films (as low as 1–2 nm) and in micro/nanostructures, both used in magnetic storage systems, micro/nanoelectromechanical systems (MEMS/NEMS). Also, Nano tribology is a branch of tribology that studies the phenomena of friction, wear, adhesion and lubrication at the Nano scale, where atomic interactions and quantum effects are important. This specialty aims to determine the properties of surfaces and modify them for both scientific and technological purposes. Al-Mustaqbal University – The First-Ranked University in Iraq Computer Engineering Technologies Department Ass.prof. Dr. Abdullah Jabar Hussain