The Set

Around the year 2350 the humanity has conquered the Milky Way Galaxy. Well, not exactly. Out of the 300 billion stars, there are just about 1.3 million human settlements. No sentient extra-terrestrial contact has been made. The major powers are The Empire, led by a dynasty of genetically engineered super-humans, and The Republic - an enormous bureaucratic machine, that somehow survives on the ancient democratic idea.
Despite almost 4 centuries have passed since the early industrial era, the technological progress is relatively slow. There were just a few "breakthroughs", and most historians blame it on Terra's total collapse around 2100. The human race almost seized to exist, the planet was obliterated by its own inhabitants. Luckily, at this point several colonies on nearby planets were already established. They helped saving the last people from their cradle and pushed further.
Undoubtedly, the most important discovery was the Space Folding. A theory, in the early 20th century, considered impossible due to the staggering amount of energy required, became a reality in the year 2173. Scientists found out areas in space, known as Lagrange points (a term, derived from the gravitational balancing points), where breaking the linear-movement-only laws is possible, using significantly less power. Several years later, the first ships, outfitted with Space Fold drives and coils managed to jump between Terra and planets nearby in a matter of minutes. In 3 years, the first interstellar trip to Proxima Centauri took place, marking the beginning of "The Expanse Era". In 4 decades, humanity colonized over a thousand planets and continued exponentially. The current human population is estimated to be over 30 trillion.
Nevertheless, people are still small, fragile, unsuited for space and its perils. The ships are basically big canisters with livable atmosphere. They still rely on jet propulsion for non-SF travel and maneuvering. The wars are still carried with projectiles, rockets are the most reliable and deadly weapons. Radiation and its consequences is still a major threat.
With SF-travel, the interstellar trade became possible. Trade-routes also happened to be the most valuable commodity. The control over them, to be precise. There are several bigger players, trying to stay neutral. Piracy is not uncommon.
When it comes to conflict, nothing changed since man exists. The Empire and The Republic are waging a war of attrition, spanning decades. No-one really takes the upper hand or achieves a major victory. Battles occur at any scale - from large fleets with thousands of ships, to individual skirmishes and guerrilla assaults. The two fundamental fractions control almost equal number of planets and resources, but fight over the "contested grounds". There are 2 other regions in the Milky Way - the Wildlands and the Outer belt, that have achieved a certain level of sovereignty - either by diplomacy or just fierce resistance to whoever came to claim them. These independent territories do not intervene in the war directly.
The Empire has better ships, stronger troops with very high morale (which sometimes lead to mutinies against commanders, if they are considered not to follow the Emperor's "no retreat" rule). The Republican Star Fleet (RSF) is numerous and capable to replenish any vessels lost in a very short time frame. As fleets are scattered to countless coordinates, mistakes happen - unexpected sorties, enemy ships just passing by without detecting each other, attacks from civilians or pirates, wrong mission targets, miscommunication, etc.