For one, proof of work prevents miners from creating bitcoins out of thin air: they must burn real energy to earn them. And two, proof of work ossifies Bitcoin’s history. If an attacker were to try and change a transaction that happened in the past, that attacker would have to redo all of the work that has been done since to catch up and establish the longest chain. This is practically impossible and is why miners are said to “secure” the Bitcoin network.
Steve Wright and John Stoll: The Dam Masters Wright, left, and Stoll, pictured at the Rocky Reach Dam, are general manager and head of customer utilities with the Chelan County Public Utility District, respectively. In the past year, miners have made inquiries or requests for power totaling two-thirds as much as the basin’s three county utilities now generate. | Patrick Cavan Brown for Politico Magazine

Bitcoins can be accepted as a means of payment for products sold or services provided. If you have a brick and mortar store, just display a sign saying “Bitcoin Accepted Here” and many of your customers may well take you up on it; the transactions can be handled with the requisite hardware terminal or wallet address through QR codes and touch screen apps. An online business can easily accept bitcoins by just adding this payment option to the others it offers, like credit cards, PayPal, etc. Online payments will require a Bitcoin merchant tool (an external processor like Coinbase or BitPay). 
The best mining sites were the old fruit warehouses—the basin is as famous for its apples as for its megawatts—but those got snapped up early. So Miehe, a tall, gregarious 38-year-old who would go on to set up a string of mines here, learned to look for less obvious solutions. He would roam the side streets and back roads, scanning for defunct businesses that might have once used a lot of power. An old machine shop, say. A closed-down convenience store. Or this: Miehe slows the Land Rover and points to a shuttered carwash sitting forlornly next to a Taco Bell. It has the space, he says. And with the water pumps and heaters, “there’s probably a ton of power distributed not very far from here,” Miehe tells me. “That could be a bitcoin mine.”
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.
Nobody owns the Bitcoin network much like no one owns the technology behind email or the Internet. Bitcoin transactions are verified by Bitcoin miners which has an entire industry and Bitcoin cloud mining options. While developers are improving the software they cannot force a change in the Bitcoin protocol because all users are free to choose what software and version they use.

Bitcoin may react differently to inflation/deflation: Bitcoin differs significantly from fiat currencies, due to the fact that there is a limited number of bitcoins to be mined. Paper money, on the other hand, can be created at will out of thin air by central banks. Due to its limited supply, Bitcoin may potentially hold its value better than paper money, which can technically have an unlimited supply.

Bitcoin has been criticized for the amount of electricity consumed by mining. As of 2015, The Economist estimated that even if all miners used modern facilities, the combined electricity consumption would be 166.7 megawatts (1.46 terawatt-hours per year).[129] At the end of 2017, the global bitcoin mining activity was estimated to consume between one and four gigawatts of electricity.[202] Politico noted that the even high-end estimates of bitcoin's total consumption levels amount to only about 6% of the total power consumed by the global banking sector, and even if bitcoin's consumption levels increased 100 fold from today's levels, bitcoin's consumption would still only amount to about 2% of global power consumption.[203]
How hard are the puzzles involved in mining? Well, that depends on how much effort is being put into mining across the network. The difficulty of the mining can be adjusted, and is adjusted by the protocol every 2016 blocks, or roughly every 2 weeks. The difficulty adjusts itself with the aim of keeping the rate of block discovery constant. Thus if more computational power is employed in mining, then the difficulty will adjust upwards to make mining harder.  And if computational power is taken off of the network, the opposite happens. The difficulty adjusts downward to make mining easier.

Bitmain acquired this mining facility in Inner Mongolia a couple years ago and has turned it into one of the most powerful money factories on the Bitcoin network. It quite literally metabolizes electricity into money. By my own calculations, the hardware on the grounds—some 21,000 computers—accounted for about 4 percent of all the computing power in the Bitcoin network when I visited.
The other two BitFury mines are in Tbilisi, in the Republic of Georgia, where the weather is much warmer. According to Vavilov, the company has developed a two-phase immersion cooling technology with their subsidiary, Allied Control. The system bathes the mining machines in a dielectric heat-transfer liquid called Novec, which cools the computers as it evaporates. The system is now deployed at the Georgia data centers.
In 2014, researchers at the University of Kentucky found "robust evidence that computer programming enthusiasts and illegal activity drive interest in bitcoin, and find limited or no support for political and investment motives".[127] Australian researchers have estimated that 25% of all bitcoin users and 44% of all bitcoin transactions are associated with illegal activity as of April 2017. There were an estimated 24 million bitcoin users primarily using bitcoin for illegal activity. They held $8 billion worth of bitcoin, and made 36 million transactions valued at $72 billion.[227][228] A group of researches analyzed bitcoin transactions in 2016 and came to a conclusion that "some recent concerns regarding the use of bitcoin for illegal transactions at the present time might be overstated".[229]

In the blockchain, bitcoins are registered to bitcoin addresses. Creating a bitcoin address requires nothing more than picking a random valid private key and computing the corresponding bitcoin address. This computation can be done in a split second. But the reverse, computing the private key of a given bitcoin address, is mathematically unfeasible. Users can tell others or make public a bitcoin address without compromising its corresponding private key. Moreover, the number of valid private keys is so vast that it is extremely unlikely someone will compute a key-pair that is already in use and has funds. The vast number of valid private keys makes it unfeasible that brute force could be used to compromise a private key. To be able to spend their bitcoins, the owner must know the corresponding private key and digitally sign the transaction. The network verifies the signature using the public key.[3]:ch. 5