What are the different elements of the gas and electricity tariffs?

There are three categories of costs that define the the price you pay for your gas supply:

Gas price: this is the price you pay to the gas supplier per m³ of natural gas that you consume. On top of that you pay a monthly service price (called prime de puissance on your invoice) which is calculated according to the capacity installed at your house. These two cost elements go to the energy supplier.
Distribution network costs: this part of your energy costs is related to the network operator, this to the company that transports the gas via its grid from the distribution point to your home. The amount is being collected by your energy supplier who transfers it to the network operator. The cost compounds a variable fee calculated according to your actual consumption and a monthly base fee (called redevance mensuelle) which you pay for having access to the network. Unlike the energy supplier who you can choose freely, your network operator is by default the company in charge of the grid at your location.
Taxes and legal fees levied by the State: you pay taxes on the consumption of natural gas, the CO₂ tax as well as VAT on the total amount of your bill.

The price you pay for your electricity has three main components, of which only one is determined by your energy supplier:

The actual electricity price: this is the price that your supplier, in this case SUDenergie, charges to finance the supply and marketing of the electricity you consume. This price consists of a variable part which is calculated according to your consumption as well as a fixed monthly fee (called prime mensuelle).
Taxes and legal fees levied by the State: each consumer pays a tax on their electricity consumption and contributes to the compensation mechanism (called mécanisme de compensation). The amount of taxes and legal fees varies depending on your consumption.
Fee for using the grid (tarif d’utilisation du réseau): this part is up to the grid operator who transports electricity from production sites to your home. Network costs and the fixed monthly fee (which includes, among other things, meter rental and which is called redevance mensuelle fixe) are approved by the Luxembourg Regulatory Institute (ILR).