Iquitos is the best place from which to embark on an adventure into the Peruvian Amazon. It's not as easy to get to as Peru's other two jungle hubs (Puerto Maldonado and Pucallpa) but compensates for that by being a much more attractive place to spend time in.
With roads out of the equation, the two ways in are by air or by a far-longer but far-more memorable adventure involving road and river. See this article for a 17-day itinerary from Lima through northern Peru to Iquitos.
Duration: 1.75-2 hours
Arriving in Iquitos from Lima by plane is, understandably, by far the most popular option, as well as being the most convenient. It is also not considerably more expensive than the more adventurous means of arrival detailed below, once all costs are factored in.
Several airlines offer flights between Lima and Iquitos. These flights operate daily, between 5:30 am and 9:30 pm, (although there are no flights at all between 12:30 pm and 6 pm). Latam has the most direct departures, with Peruvian and Star Perú also offering direct flights.
The airport in Iquitos, Coronel FAP Francisco Secada Vignetta airport, is about 25 minutes to the center of town by taxi and mototaxi (three-wheeled motorcycle).
By Flight, Bus, or Private Transfer and Boat
Duration: 1.5-4.5 days
Getting to the world's biggest city not to be connected by road can, of course, be a very big adventure. The very factor which makes it so difficult to build a road to Iquitos is what makes a journey there so epic: the jungle.
Going to Tarapoto by plane is the quickest way to start the adventure, a 1.5 hour flight from Lima. There are six or seven direct flights daily. The second part of the journey is by bus or private transfer to the jungle city of Yurimaguas (2-2.5 hours). Transport for this part of the journey leaves throughout the day.
In Yurimaguas, you can board a boat traveling downriver on the Rivers Huallaga, Marañon, and Amazon to Iquitos on the third part of the journey. Boats come in many shapes and forms and leave usually in the early morning only. Going the quickest (and most expensive) way, fast boats travel to Lagunas (4-5 hours) where you can change for another fast boat to Iquitos (9-10 hours). Travel times do not always connect, meaning you might have to overnight in Yurimaguas, Lagunas or both.
Obviously, the advantages of such a journey are not the efficiency, but the insights you get into local life along the way. These are particularly colorful on the river part of the journey.
By Private Transfer or Bus and Boat
Duration: 2.5-5.5 days
Taking you up along the desert coastline and over the forested highlands before plunging you deep into the heart of the Amazon rainforest, this is the cheapest and least efficient way to get to Iquitos. Note that it is cheapest by price of the transport alone, but on this long journey you will almost certainly need to pay for overnight accommodation also.
The first part of the journey is by road to Tarapoto (26-29 hours): buses normally depart from Lima in the evening and go overnight. Because of the distance, bus is recommended for this stage. The second and third parts are exactly the same as for the previous option.