Pest Control

Sucking Pests 
Sucking pests refers to anything that lives above the ground and feeds on the sap or soft tissues of leaves, stems, and flowers. There are three main ways to deal with sucking pests: manual removal, leaf sprays and systemic treatments.
Manual Removal
The simplest solution is sometimes the most effective. We've found that manual removal is particularly effective for mealy bugs and spider mites. 
For mealy bugs, a Q-tip dipped in rubbing alcohol (although a dry one would work just as well) to physically remove the visible mealy bugs over the course of a week or two will drastically reduce if not eliminate the pest population. 
Spider mites are very small and light and therefore easily dislodged. A simple shower with a stream of water (be sure to get underneath each leaf!) every day for a few days can remove both adults and juveniles. We've noticed that dehydrated and stressed plants (such as tropicals kept in low humidity) are particularly susceptible to spider mites, which makes the showering approach a double edged sword. 
Leaf Sprays
Leaf sprays are the simplest and most common method of pest control for indoor plants. Pyrethrins are highly efficient for spider mites, thrips (only certain life stages), mealy bugs, white flies, and aphids. Use caution when spraying pyrethrins as they are mildly toxic when inhaled, and only spray where there is good air circulation, or better yet outside. Pyrethrin will persist on a leaves for a period, preventing reinfestation. 
A less toxic alternative is neem oil as a foliar spray. Neem oil remains on the leaves to keep bugs away for a period, similar to pyrethrin. Because it is an oil, Neem oil should be mixed with soap in lukewarm water in a spray bottle before application. The soap works both to mix up the oil and also to kill the bugs directly on contact. A repeated treatment (we recommend every few days) will be most effective with foliar sprays. 
Care should be taken to protect sprayed leaves from light, as they are particularly sensitive while wet. We always recommend spraying in the evening after the sun has set to allow plants a full night to dry and recover from any potential stress caused by the pesticides. 
The final method of dealing with sucking pests is more of the 'nuke it' approach, and this is systemic pesticides. We recommend only using this for extreme cases, and particularly only using it on indoor plants where risk of pollinator exposure is minimized. This is because most systemic insecticides contain the active ingredient Imidacloprid, a neonicotinoid which can persist for years in soil and is believed by researchers to be a contributing factor in the falling bee populations worldwide. 
While a slightly higher-consequence pesticide, systemics can be an excellent peace of mind for those of us dealing with extreme or repeat outbreaks. 
Ofcourse, always follow all manufacturer warnings and only use pesticides as directed! 
Root pests 
Root pests chew or suck on plant tissue, similar to above, however they do their damage under the soil. This makes it more difficult for us to identify and also to treat. Luckily, many of the treatments used as foliar sprays can also be used to deal with root pests. 
Possibly the most common tropical houseplant pest among hobbyists is the fungus gnat. These are the tiny black fruit-fly like things that fly in annoying mindless loops around your house and seem to always target your eye when you're reading a book…. 
Soil soaks
Fungus gnats thrive in consistently wet soil, and therefore are particularly annoying for those of us who collect moisture loving plants such as bromeliads, calathea, and some philodendron. They lay their eggs in soil and hatch when it's sufficiently moist, releasing larvae that wriggle around in the soil feeding on decaying organic matter including damaged or rotting roots. When they're a couple weeks old they pupate and become the annoying flying bugs we are familiar with. 
A very simple way to deal with fungus gnats in houseplants is to allow the soil to dry out slightly (at least the topmost two inches or so) between waterings. While this may cause stress damage in species like Calathea, some such as philodendron may appreciate a slight drying more than we expect. 
Another treatment for gnats is the Neem soil soak. Make a mix with insecticidal soap similar to for a foliar spray and thoroughly soak the soil until the solution comes out the drainage holes, follow with a water rinse, then allow to dry as much as the specific plant allows. 
Soil alternatives 
For thrips, which have certain life stages dormant in the soil, as well as fungus gnats, completely changing the soil and replacing with a sterile clean batch is an excellent way to cut their population in half (or more). Alternatively, switching to hydroponic or semi-hydroponic systems for plants that allow it (most tropicals and many succulents as well) will eliminate the risk of soil-dwelling pests entirely. 
Systemic pesticides 
Similar to sucking pests, neonicotinoid pesticides such as imidacloprid can be used to protect the roots. This prevents fungus gnats, grubs, or other root-chewing pests from eating your roots, however will not be very effective against dormant stage insects such as thrips in soil. 
As mentioned above, please be aware of the risks and consequences of using neonicotinoid pesticides if considering this route. 
Sticky Traps
Yellow (fungus gnats) or blue (thrips) sticky traps are a cheap and effective defense against flying insects. While usually not enough to eliminate an outbreak altogether, they make an excellent second line of defense to catch adults before they can breed. We personally keep these all over our planty areas and find there's always a few stragglers that survive other treatments but get caught by these. 
Overall, there are many different ways to deal with any type of pest so there is no need to panic when you notice something munching on your favourite plant. 
Our favourite strategy is to maintain a strong defense with regular plant showering (each time we water), spraying of mild chemicals (a biweekly spray of neem oil mixed with insecticidal soap - this works as a leaf shine too!), and blue and yellow sticky traps scattered throughout the house in pots. 
When we do notice an outbreak (it happens to the best of us), we will up the frequency of Neem treatment (sometimes this is enough) and do a foliar pyrethrin spray every several days for a week. In our experience this is enough to deal with 99% of pest issues without resorting to harsh chemicals such as neonicotinoids.