Periodization is often a slippery issue in historiography as the its rationale can range from very arbitrary to highly specific. In the case of Napoleon, the importance of his military fortunes to his empire also meant that historians who studied the period gravitated towards military affairs and issues of international diplomacy. This differed markedly with historians of the Revolution who tended to focus on issues of ideology and solving the riddle of why the Terror happened. Older historical scholarship such as Georges Lefebvre has tended to treat the coup of Brumaire as the formal end of the Revolution when France turned away from the liberal democratic impulses of the Revolution. There is a strong tradition in Marxist and Marxist-influenced scholarship that treats Brumaire as the capstone for final victory of the bourgeoisie as they consolidated their political hegemony within France through their sponsorship of Napoleon. This particular interpretation built on Marx's own Eighteenth Brumaire that contrasted the events of Napoleon with that of his nephew and the idea of Napoleon as the end of the Revolution remained solidly entrenched as the orthodox interpretation of the Revolution for a good deal of the twentieth century and still remains somewhat common.

However, this interpretation of Napoleon as the end of the Revolution has come under increasing attack by scholars that see Napoleon as a continuation of the Revolution. Francois Furet, building upon de Tocqueville's critiques of the Revolution, argued that Napoleon's dictatorship was the epilogue of Revolutionary principles and ideas in which Napoleon consolidated the Revolution's tendencies to use democratic rhetoric for despotic ends. Other historians like Isser Woloch and Howard Brown argue that there was significant continuity between Napoleon's regime and the Revolution in its personnel and the attitudes of the elite to social control. The continuity thesis has also benefited from the turn away from high politics to issues of everyday life, the structuring of society, and specific cultural issues like gender or military culture. These types of histories frequently take a long view of history which tend to make the changes in political regimes appear less salient to the conduct of people's daily lives.

One of the underlying causes for the murkiness of this issue is the highly contradictory nature of Napoleon himself and how he styled his dictatorship. After Brumaire, he presented himself both as the culmination of the Revolution and a decisive break with it. Political opponents from both the monarchist and the Jacobin factions attacked Napoleon's dictatorship as either a culmination or betrayal of the principles of 1789.

To add to /u/kieslowskifan, Napoleon is both but since we're talking about an individual, there are different stages, just as Beethoven has a Early, mid, and late era of composition.

Napoleon before to Eighteenth of Brumaire is considered a part of the Revolution. He pushed Republican ideals in Italy and tried to weaken Britain with a poorly thought out Egyptian adventure. These fit into the Revolutionary Wars since Napoleon, serving as a Lieutenant, Captain, and General of the French Republic, was fighting in these wars and did not have a direct say (a minor exception of Egypt) of the political or military direction of France (although he still ignored the Directorate).

The Napoleonic Era of French history often slides into the French Revolution as /u/kieslowskifan mentions and does good to fit within the historiography but it must be stated that Revolutionary France is the Revolution under others, Napoleon's ascension to First Consul marks the beginning of France ruled under Napoleon. It also must be noted that it is effectively a direct rule. He hamstrings the legislative bodies in order to control them and prevent anything happening that isn't directly influenced by him. The Executive side of the French government was more or less a plateau that reported directly to him (or Berthier, his Chief of Staff).

However, for ease of education (and laziness), most world history text books teach the Revolution as part of the Napoleonic Era, fitting into a Great Man theory of history that isn't in favor within academic historiography.