How to charge Lithium batteries?

Very typical question I receive in my email: How do I charge Lithium battery?
In brutal honesty, it means to me that inquirer is in the early stage of getting to know Li batteries.
Nothing wrong with that, except there are lots of nuances in this topic. Failure to comply with them will lead to destruction of the battery and chances to have explosion or fire.
Therefore I'm facing rather difficult choices.
I could politely defer person to another source of knowledge and possibly deny purchasing from visbis.com. Reason for that because I take chances to be potentially accused of not properly teaching about Li polymers {or any Li batteries to that extend} AND possibly being accused our batteries are "bad" because they "didn't work" or worked only for very short time.
In 99.9% cases, the fault is on user side because of wrong usage or charging technique.
I will try to be on the generous side and will try to give little bit condensed knowledge here about charging Li batteries. BUT! Heavy disclaimer! Author of this wring giving the material for light education and entertainment reason! Please enter Li battery world and this material with caution.

How do I do charging in my lab: I take Cadex charger and connect to it. Or in most of times I take lab power supply, tune max current and max voltage (4.2V) and connect battery.

This is typical Cadex battery charger and tester.

Ok, for those who survived given above disclaimer, I shall be more diligent.
1. All Lithium batteries can be divided on Rechargeable and Non Rechargeable.
If battery NON rechargeable, please stop reading on how to charge those. Charging Non rechargeable will lead to "ca-bum!"
If you wonder which is which, please go to this articles about types of batteries and firmly determine what battery is in front of you.

2. If battery is Lithium Rechargeable, you need to determine base chemistry of the battery. Only then you could proceed to charging technique.
Most of Li-rechargeable batteries on the market are Li-polymer or Li-po or Li-ion. For those charging method is well known and IF you do not make your own devise with it's internal charging circuitry inside, you could always find something on aliexpress or ebay or amazon.
For all generic Li-po or Li-ion batteries (normally they are Li-cobalt or LiCoO2)  you will need CC (current limiting) power source with 4.2V maximum voltage.

Picture above is typical charge curve. Please pay attention on 95% charge state region. Curve is tapering off at 4.2 volts.
For all generic Li-iron phosphate or LiFePo4 you have to limit your voltage to 3.65 volts. At 3.5V LiFePO4 reaches 95% of charge level. After that charging process is very slow and reaches 100% charging level at 3.65V. Charging currents again shall be limited to what battery model recommend and in most of time it is 1C max.

This is typical LFP )LifePO4) battery with 5Ah capacity charge-discharge curve. Please note 0A and 5000mA regions. Lots of information is there.
In the charging procedure you need to be in two boundaries: your Charging Voltage shall never be over 4.2 volts and your Charging Current shall not exceed manufacturing specified current. Normally for generic Li-po battery it is between 0.2C/h and 0.8C/h. What is that C deal is all about? All batteries has Capacity parameter.
For example this battery GM300910 has 8mAh capacity. Therefore factory said you shall be not over 0.8C or =6.4mA charging current. Can you charge with 10mA this battery? Yes, you can. But then we can't guarantee you long battery life. Frankly lots of people charging with 2C currents, and get away with that. It means the devise is getting "fully" charged within 30 minutes instead of 1.5 hours. Then don't complain about 2-3 months of usage of your device.
So, to summarize what I said: Voltage should be limited to 4.2V and current limited to 0.8C.
 What will happened if I continue to charge with 4.3V? Battery will be destroyed. ALL Li batteries are VERY sensitive to charging parameters. With even 0.1 volt more, you will lead to fast destruction of the battery and 0.5V will lead to explosion. So if you put 5V usb voltage directly to battery and charge it to "complete", it will lead destruction.
If you interested in Li-Titanate or Li-Silicade or any other chemistries, this is beyond this simplified article for the beginners and we will discuss this in more advanced article.

3. Environmental Temperature during charging is critical. You shall never charge Li ion, li polymer or Li iron phosphate batteries below 0C. Do below 0C charging and you instantly get damaged battery.
Also charging above 45C is very rapidly deteriorate lithium battery. After 65C charging battery lead to fast destruction.
Many customers looking for batteries for Solar systems. This is very challenging questions. Most of solar devises outside of temperature controlled environment. In winter, they are below 0C, in summer they are getting close to 100C on the sun. I don't have a simple answer. Yes, there are many tricks to make your design happened for outside of house usage. But most of answers lay in to financial plane. Without 5000usd(rough figure) all answers are not economically viable.