I was looking at the block #339174 on blockchain.info "unconfirmed-transactions" there were over 3350 unconfirmed transactions.
It took 49 minutes to solve this block & the size was over 1700kb. The block size after solved was 487.27KB & 1549 transactions were confirmed.
What happens to the other 1800 unconfirmed transactions? Do they have to wait until the next block or even longer? It seems the large block size is delaying transactions more and more right?
Each miner/mining pool decides which transactions go into the block they are trying to solve. Transactions that are not included in a block are available to be included in the next block. Again, whether or not they are included in the next block is up to each miner/mining pool.
As has already been stated, the size of the block does not determine how long it takes to solve, though longer times between blocks generally result in bigger blocks.