Overall when considering the inflammatory response, one must remember that this is a complex biological protection that the body uses against foreign invaders that involves not only the innate but also the adaptive immune systems. The hallmarks of inflammation were originally noted by Celsus, a Roman physician, who stated " rubor et tumor cum calore et dolore" which translates into what we know today as "redness and swelling with heat and pain". This was added with the additional hallmark by Galen who stated " functio laesa" which translates into "loss of function" which is due to both pain and swelling.
Inflammation usually falls into two categories such as being acute inflammation such as seen in infection and the healing process which is short term or chronic inflammation (very very bad) which is long term and not resolved which is normally seen in IBS, cardiovascular disease, and type-2 diabetes. As mentioned above, the characteristic signs of inflammation we know today function in part because they increase vascular diameter (vasodilation) which causes a rise in blood volume. This blood volume rise heats the tissue and causes it to redden. Along with this vascular permeability also increases which leads to increasing leakage of fluid from the blood vessels leading to edema or swelling.
When localization of infection, tissue damage, or harmful chemical exposure occurs sentinel cells that reside in the epithelial layer which consist of macrophages, mast cells, and dendritic cells-become activated by PAMPs, DAMPS, etc and begin the process of phagocytosing the foreign invaders. These calls are also activated by the PRR signaling pathway that causes releasing of innate immunity mediators such as cytokines and chemokines that cause numerous processes to unfold that collectively contribute to the inflammatory response.
As mentioned above, PRR signaling activates resident macrophages, mast cells, and dendritic cells to release innate mediators which are proinflammatory cytokines TNF-alpha, IL-1Beta, IL-6; chemokines; prostaglandins; and histamine amongst the rest. These in turn, act on the vascular endothelial cells of surrounding blood vessels to increase vascular permeability and the upregulation of cell adhesion molecules or CAMs along with chemokines IL-8, the tissue being affected is now inflamed or activated.
Fluid enters the tissues to deliver antimicrobial molecules that include complement proteins that result in swelling or edema. Cells that are presently flowing in these blood vessels are affected by the inducing effect of chemokines and cell adhesion molecules for vascular endothelial cells adherence to allow cellular passage from the capillaries into the inflamed tissue through a process called extravasation (this process is just mentioned here and not discussed in detail).
In this course of inflammation, neutrophils are the first cells to be recruited to the site of infection or tissue damage in which they allow for the enhancement of the local innate responses. This is then followed by the recruitment of monocytes that differentiate into macrophages that in turn continue to contribute to the clearing of pathogens and cellular debris and contribute to innate healing of the wound. The early produced cytokines (TNHF-alpha, IL-1Beta, IL-6) contain systemic properties that include production of fever by inducing COX2 production that causes prostaglandin synthesis. Prostaglandins E2 affects the hypothalamus to cause fever. The proinflammatory cytokines TNF-alpha, IL-1Beta, IL-6 affect the liver to induce the acute-phase response that forms in the production of liver proteins (opsonins and MBL) that contribute to pathogen elimination and resolution of the inflammatory response.
*This only covers the inflammatory response seen in skin invasion the inflammatory response in the lungs and mucus membranes such as the intestinal tract are similar but contain adequate differences and are not the scope of this expert answer. If wanting to learn more about these feel free to private message me and we converse over tutoring.