User fear of 51% attacks can actually limit monopolies from forming on the blockchain. In “Digital Gold: Bitcoin and the Inside Story of the Misfits and Millionaires Trying to Reinvent Money,” New York Times journalist Nathaniel Popper writes of how a group of users, called “Bitfury,” pooled thousands of high-powered computers together to gain a competitive edge on the blockchain. Their goal was to mine as many blocks as possible and earn bitcoin, which at the time were valued at approximately $700 each.
Newer cryptocurrencies and blockchain networks are susceptible to 51% attacks. These attacks are extremely difficult to execute due to the computational power required to gain majority control of a blockchain network, but NYU computer science researcher Joseph Bonneau said that might change. Bonneau released a report last year estimating that 51% attacks were likely to increase, as hackers can now simply rent computational power, rather than buying all of the equipment.
In Bitcoin, it’s like every organic food store has someone out front, offering free samples. Also, there’s a library everywhere you look, but only a few of those libraries have any good information. The largest traders would benefit a great deal if everyone just jumped blindly into Bitcoin, investing large chunks of their life savings in the process. That would be just fine by them, but it’s unlikely to happen. More likely, people are going to get involved with Bitcoin either by necessity, by chance or because someone was willing to give them a few bitcoins to get started with.
Since bitcoin mining has become a hardware intense and therefore expensive process, most individual miners join a so called mining pool. One of the mining pools you can conect to is BitMinter for example. By providing computing power to their pool you can earn Bitcoins from mining without the need to build your own big mining farm. There are entire communities around Bitcoin mining and besides the fact that you earn Bitcoins it's also fun. You meet new people online and get in-depth knowledge about Bitcoin as a protocol and technology.
Regarding more practical concerns, hacking and scams are the norms. They happen at least once a week and are getting more sophisticated. Bitcoin’s software complexity and the volatility of its currency dissuade many people from using it, while its transactions are frustratingly slow. You’ll have to wait at least ten minutes for your network to approve the transaction. Recently, some Reddit users reported waiting more than one hour for their transactions to be confirmed.
Illiquidity. This is mostly moot due to Bitcoin’s $47 market cap but it still makes users sweat. It’s highly unlikely that Bitcoin’s price would plummet and you’d be unable to take action, but it’s still unsettling.  As more investors invest, however, illiquidity becomes a negligible risk, as there will likely always be a buyer for Bitcoins waiting.
The use of bitcoin by criminals has attracted the attention of financial regulators, legislative bodies, law enforcement, and the media.[217] In the United States, the FBI prepared an intelligence assessment,[218] the SEC issued a pointed warning about investment schemes using virtual currencies,[217] and the U.S. Senate held a hearing on virtual currencies in November 2013.[219] The U.S. government claimed that bitcoin was used to facilitate payments related to Russian interference in the 2016 United States elections.[220]

The good news: No advanced math or computation is involved. You may have heard that miners are solving difficult mathematical problems--that's not true at all. What they're actually doing is trying to be the first miner to come up with a 64-digit hexadecimal number (a "hash") that is less than or equal to the target hash. It's basically guess work.

Though each bitcoin transaction is recorded in a public log, names of buyers and sellers are never revealed – only their wallet IDs. While that keeps bitcoin users’ transactions private, it also lets them buy or sell anything without easily tracing it back to them. That’s why it has become the currency of choice for people online buying drugs or other illicit activities.
Transactions are defined using a Forth-like scripting language.[3]:ch. 5 Transactions consist of one or more inputs and one or more outputs. When a user sends bitcoins, the user designates each address and the amount of bitcoin being sent to that address in an output. To prevent double spending, each input must refer to a previous unspent output in the blockchain.[69] The use of multiple inputs corresponds to the use of multiple coins in a cash transaction. Since transactions can have multiple outputs, users can send bitcoins to multiple recipients in one transaction. As in a cash transaction, the sum of inputs (coins used to pay) can exceed the intended sum of payments. In such a case, an additional output is used, returning the change back to the payer.[69] Any input satoshis not accounted for in the transaction outputs become the transaction fee.[69]