It consist of constant current boost converter LT1618, Li-Ion USB charger MCP73831, UVLO circuit with comparator MCP65R41T, USB current limiter BL2554 and charging indicator circuit. Cathode of the LED can be connected either to the ground or to the positive rail. The first way is best for systems where the battery voltage is always lower than LED voltage. In this case, the converter always acts as simple boost converter. But in the case you want to power a typical 3.5V white LED with constant current from single 3.7V Li-Ion cell (whose voltage is 4.2V when fully charged and 2.7V when discharged) then it is better to connect the cathode of the LED to the positive terminal of the battery. This creates a virtual buck-boost converter. LED current is set by R8. Voltage drop across this resistor is 50mV and with R8 = 0,16Ohm, the LED current is 312mA. UVLO threshold is set by resistors R4 and R5 to around 2,8V. R6 and D2 provide strong hysteresis.