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Does the Monero block reward just decrease and I don't mean the transaction fee. Are there any specific dates of this when it will happen?

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Monero has a "smooth" emission. This means the block reward decreases gradually until it hits 0.3 XMR per minute. Subsequently, the tail emission kicks in and the block reward will remain 0.3 XMR per minute indefinitely. This will occur in approximately 2023. Note that the tail emission is not inherent to CryptoNote, but was specifically implemented in Monero.

In the CryptoNote whitepaper the emission is described as follows:

6.1 Smooth emission

The upper bound for the overall amount of CryptoNote digital coins is:

MSupply = 2^64 − 1 atomic units.

This is a natural restriction based only on implementation limits, not on intuition such as “N coins ought to be enough for anybody”. To ensure the smoothness of the emission process we use the following formula for block rewards:

BaseReward = (MSupply − A) >> 18

Where A is amount of previously generated coins.

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    Note that that was for 1 min block interval. It has been adjusted accordingly with the move to 2 min block interval. – JollyMort Apr 18 '17 at 14:52

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