Darien Gap

The Darién Gap (Spanish: Región del Darién or Tapón del Darién) is a break in the Pan-American Highway consisting of a large swath of undeveloped swampland and forest within Panama's Darién Province in Central America and the northern portion of Colombia's Chocó Department in South America.

Understand
The gap measures just over 160 km (100 mi) long and about 50 km (30 mi) wide. Road building through this area is expensive, and the environmental cost is high. Political consensus in favor of road construction has not emerged. Consequently there is no road connection through the Darién Gap connecting North America with South America and it is the missing link of the Pan-American Highway.

Since this area is the only piece of land connecting both continents, it is dominated by drug cartels.

The overland crossings are considered to be hard and dangerous.

Flights
The best option is to fly to Medellín. AirPanama offers cheap flights for around $130.

From Medellín to Cartagena you can take: Of course prices depend on how long before the flight you book it, but it stays fairly close to this amount even a couple of days before the planned flight date.
 * Bus – 11 hours and around 30$
 * VivaColombia flight – 1h and around 30$

"Overland"
Not precisely overland since there is one flight and several boat rides involved.

Buy plane tickets a day in advance from the AirPanama agency that is inside the terminal of Alboork Airport. From Panama City to Puerto Obaldía. Do not book it online, they do not have the best system and this flight is not perfectly scheduled. Even on the website they will warn you about booking it.
 * Buy plane tickets

Puerto Obaldía is a small town on the Caribbean shore of Panama a couple of miles from the border with Colombia. It is not accessible by any road. Though there are no scheduled boat services, there are boats going there infrequently from the Cartí Port, one of the ports to get to the San Blas Islands. It only has a small airport. You can stay around here though it is pretty ugly and not perfectly safe.
 * Panama City–Puerto Obaldía (75$)

The plane is small and has a baggage limit of 10kg with a 1.5$ fine for any kg more. So pack light, actually you are going to meet your container shortly after you get to Cartagena so there is no reason to not pack light. Make sure you know the weight of you baggage before because they try to scam you and charge more. As soon as you land, go to immigration to exit the country and book your boat to Capurganá, it leaves couple of hours after the flight lands.

Capurganá is the same idea as the last one just on the Colombian side of the border. It is heavily guarded by law enforcement so it is safer and it is actually a nice town to relax and enjoy the nothingness on a Caribbean beach served by a couple of small hotels. You might have to spend the night here anyway waiting for the boat to turbo. Boats leaves hourly from morning to sundown and weight deal of the baggage applies here as well.
 * Puerto Obaldía–Capurganá (15$)

You will go through immigration here, make sure you get all the paperwork right.

There is apparently only one boat a day leaving on the morning, so make sure you book your boat as early as you get to town to reserve your seat on the boat. It is a speed boat and the trip takes 3–4 hours along the jungles of the Darien Gap going straight into the Caribbean water. Try to show up early for the boat to get a nice spot on the back of the boat so you won't get all wet. Get your camera ready.
 * Capurganá–Turbo (30$)

Boats go frequently from Capurganá to Necoclí, a town a few hours north of Turbo.
 * Capurganá—Necoclí

Vehicle
International Vehicle Shipping Services and Overland Embassy offer vehicle transportation through the Darien Gap.

General tips

 * Get Colombian Pesos in Panama City since ATMs are not to be found until you get to Turbo and the exchange rate is pretty bad.
 * Get ready to get wet on the boats! A rain coat and something to cover your luggage will be good.

Go next
From Turbo's central bus station you can find buses to
 * Medellin
 * Cartagena - 5 hours to Montería and from there 5 hours more to Cartagena