L-Theanine & Caffeine combination is one of the safer and most popular nootropic stacks out there. Most of the time, it is what people start with when experimenting with nootropics due to its simple understanding, profound effect, and vast availability of data.
The typical combination ratio is 100mg caffeine to 200mg L-theanine.
A central nervous system stimulant. It is also the world's most widely consumed drug. Humanity is a mass of junkies, but that's off-topic. On the other hand;
An amino acid found in certain plant species, and mostly known for being one of the compounds of green tea. You can read more about L-theanine as a nootropic here.
Taking more than one nootropic at a time (2 or more) because they synergize well together, increasing and complementing one another's effects.
The creation of something that is greater than the simple sum of its parts – (nice definition, I had to throw it in there).
When we hear of caffeine, the first thoughts that pop in our heads (and to many, the only) are something along the lines of stimulants, energy, wakefulness. Most people tend to overlook the actual benefits of caffeine. Not necessarily the 6 pumps vanilla sugar-filled chocolate drizzle frappuccino. What I refer to here is caffeine in its pure form, the chemical, central nervous system stimulant.
Some examples of the less known health benefits of caffeine:
- Caffeine boosts memory and especially memory consolidation, as shown in a Japanese study at Johns Hopkins University.
- Caffeine stimulates hair growth (in blading men and women). 
It also reduces mouth and throat cancer risk by 50%, reduces the risk of stroke by as much as 22%, and even decreases the risk of type diabetes. The list goes on and on but we are more focusing on the nootropic, cognition-related benefits. Some of which are the following:
- Boosts overall memory, as well as formation and especially memory consolidation. 
- It fights erectile dysfunction and increases semen volume  
- Improves reaction time and logical reasoning, especially in sleep-deprived individuals. 
- Boosts energy as well as athletic performance, and weight training. 
That, of course, doesn't mean it doesn't have a negative side to it though.
L-theanine, on the other hand, is much less known comparing to caffeine. But it is very well known to those within the nootropic community.
Although it is existing in green tea, the concentration is too low to produce notable nootropic effects. Therefore, nootropically speaking, a higher concentration of l-theanine is required than that found in green tea for example. Which is what led to the production and widespread l-theanine supplement in capsule form.
L-theanine benefits include promoting relaxation and contributing to better sleep quality. Moreover:
- It boosts GABA, serotonin and dopamine levels in the brain, as well as lowers excitatory chemicals. Thereby, L-theanine reduces stress and anxiety.
- Enhances attention, focus, and learning ability.
- Improves sleep quality
The Synergy Effect
Now, speaking logically, what do you think would happen if you take both caffeine and theanine together, at the same time (caffeine l-theanine stack)?
It would give you the best of both worlds:
The stimulation, alertness, and wakefulness, without the associating crash, jitters, or anxiety that often come along with or after caffeine consumption.
Due to L-theanine calming and relaxing effects, this combination is one of the most popular nootropic stacks. It is simple, and both cimound have a vast amount of studies on them. So not a lot of digging is required to pull information on them.
Combining the two together results in this, or a very similar experience. Might even be better (or worse if you're the unlucky one):
“You can concentrate on your work more thoroughly, be more creative, and achieve more success with the absence of headaches, crashes, and anxiety. The combination gives you the power to perform better than taking either alone.” 
Although newer formulations have been surfacing around, the widely known caffeine & l-theanine dosage is a 1:2 ratio. In most cases, that being:
- 100mg Caffeine
- 200mg L-Theanine
My Personal Experience
I don't respond very well to coffee. I love it but its the unforbidden love to me because too much caffeine intake increases my hyperactivity. But when it comes to caffeine/theanine combo, it seems to take care of that and lead me to a hyper-focus state. Especially given that I'm ADHD, I can get very engaged into something and lose track and sense and even existence of time all together.
However, although I have caffeine/theanine from ND, I don't really find myself using it frequently. And that is mainly due to the fact that I drink a cup of bulletproof coffee first thing after waking up. Even though the caffeine concentration is lower in my morning coffee than the common 100mg, I drink my cup followed by a 200mg L-theanine. I found that this works the best for me, allowing me to reap the benefits of both, the synergy of the two compounds, as well as enjoy my bulletproof coffee and practice intermittent fasting (in my personal dictionary, this could also mean starvation and weight loss, but let's stay on topic here).
If you would like to read more into the combination and synergy of the two compounds, you may enjoy the following studies and articles:
- ‘The effects of l-theanine, caffeine and their combination on cognition and mood‘ by the Psychology Division of Northumbria University
- ‘L-Theanine and caffeine improve target-specific attention to visual stimuli by decreasing mind wandering: a human functional magnetic resonance imaging study‘ by the Department of Nutritional Sciences, Texas Tech University
- ‘Effects of l-theanine on attention and reaction time response‘ by University of Shiga Prefecture, Human Culture Department, Japan
- Choline: All About The Essential Vitamin-Like Compound
- Phenibut: An In-Depth Review of a Powerful Nootropic Agent
- Ultimate Nootropics FAQ List