Living With Aphids
I remember the first time I encountered aphids. I had purchased some pepper plants from a nearby garden center. They sat on the balcony for a few days before I got around to transplanting them and I noticed that the newest leaves on one of the plants had a number of very tiny green succulent insects on them. I brushed off as many as I could and went ahead with transplanting the plants.

Mommy aphid and a new born nymph. An hour later I found another nymph on this leaf. I believe the black dots in the mother are the eyes of other unborn nymphs
When I checked my plants the next day, the bugs were back and this time there were twice as many and on more than one plant. Eventually every one of the dozen pepper plants had these bugs stuck to them. They tended to cling to the underside of the leaves and thrived in and around the open and unopened plant flower buds. Most of the plants failed to produce peppers and the few that did just gave me peppers that were stunted and irregularly shaped.
I didn't know what they were then but I certainly know them now. Aphids survive by sucking the juices from a plant. Some plants they like and some they don't. There are different species of aphids that prefer different plants. I did't know what mine were - I didn't really care. I just wanted to get rid of them. The problem is, they multiply at an astonishing rate. The females reproduce asexually by a process known as parthenogenesis. They do not need males to reproduce and for most of the season, all they produce are female offspring. They live between 20 and 40 days and can produce something like 5 offspring each day from the time they are a week old. Translation: huge colonies in a short amount of time.
I tried squishing them all whenever I found them but when I did I sometimes damaged the plants so I resorted to a mild mix of soap and water. I've read mixed things about what type of soap to use with some people insisting you use insecticidal soap and others using dish soap. I opted for dish soap. With a small paint brush I dabbed my soapy solution on the insects. First lightly, then excessively. Aphids typically cling to the underside of the leaves making it hard to find them all. I spent lots of time crouched over these plants and when I was finished all I did was make a mess. Much of the plants I had soaped up were now dying. And within a few days the aphids were back in full force, just like cockroaches.

This poor bambino eggplant flower, as well as the rest of the plant, was covered with aphids. The aphids love my eggplants just as much as my peppers.
My next attempt to get rid of the aphids was to blow them off the plants with a squirt bottle. In a garden, I could just blast them off with a hose but I can't do that on the balcony. The squirt bottle method worked quite well and didn't kill the plants but the affect was only temporary. I remember seeing aphids in the soil, making their way back to the stems of the plants, marching their way up to the tender new leaves at the top.
Aphids have a number of natural predators. Lady Bugs are one. Lacewing larvae are another. Neither of them show up on my balcony very often. That's the problem with growing plants in a semi-enclosed environment. Without natural predators to keep them in-check, pests like aphids thrive. Recently I've notice hover-fly larva occasionally inching their way around my plants and devouring aphid colonies. They do a thorough job but once the larva transform into flies, they leave and the aphid return.
At some point the aphid population will produce winged females who fly off to seek out a good place to start new colonies. I've read that certain colours and shinny objects can distract them and keep these winged aphids away from your plants. But I think in most cases it's just a matter of time before one makes a successful landing. In the fall, some colonies will start producing male aphids and these mate with the females. The result is aphid eggs that can survive the winter. The year after the big aphid infestation I grew peppers again, but this time from seed. And once again, the aphids were back. I'm convinced these started with hatchings from the last infestation. Fortunately I didn't put too much effort into peppers that season but the few I did grow presented me with another problem.
Aphids excrete a sweet liquid when they feed known as honeydew. It tends to attract a number of other insect species. It's easy to spot - just look for shinny wet patches on the tops of lower leaves and chances are good that there is an aphid colony on one of the leaves above it. That summer there must have been a wasps nest someplace nearby because I had this constant swarm of wasps coming onto the balcony to collect the aphid excretions from the leaves of the pepper plants. There were enough of them that we just couldn't enjoy the balcony and the season was a loss. I'd get out there to water everything but that was all. My plants got really wild and bushy that year.

The appearance of winged aphids means it's just a matter of time before you start seeing colonies on other plants, if you haven't already.
I've seen aphids almost every year since that first outbreak but not in the same numbers I first had. I spend more time washing down my containers with soapy water, particularly those that held aphid-infested plants the previous season. I also pay closer attention to plants I know aphids favour, such as peppers. The aphids also seem to like some of my annuals. I had some marigolds one year that had huge numbers of aphids but only on the flower buds and stems. Again, these were plants purchased at a garden center. Even some purple basil I got at the same place had a few aphids but they were easy to pick off and didn't persist. I'm pretty sure purple basil is not their preferred diet. I've also had them on potato and broccoli plants but they didn't seem to bother those much and the colonies didn't thrive.
One the best methods of prevention is to not accept any plant on my balcony that have aphids. Everything purchased at a nursery or garden center has to be carefully inspected. The last trick I used to get rid of them was neem oil. It didn't seem to work but it does work great for controlling spider mites and mildew. Scrubbing my containers at the start of every season works. Especially containers that are going to hold plants I know the aphids will thrive on. A healthy plant can manage with a few aphids sucking on it. On some annuals, with just the flowers and buds infested, I've pinched off the infected growth and let the plant survive. But there were some annuals I uprooted and tossed. It's unfortunate, but sometimes that's what you have to do when growing on the balcony.