| It doesn't stop|
at the water's edge
Chequebook diplomacy (or checkbook diplomacy) is a form of soft power, by the usage of aid, development funds or favourable loans by major economic or political powers to assist usually small recipient countries with various kinds of investments or developments. This is usually infrastructure such as bridges, airports, roads and public housing that support both the host and the recipient. This is done in return for diplomatic or political support by the recipient for the host country. Such action is noticeable in Pacific island states like Fiji, Tuvalu and Tonga, but also in the nations of the Caribbean and Africa.
Such diplomatic actions are often the reason why seemingly bizarre viewpoints exist in countries, despite there being no direct reason for having those viewpoints in the first place. Such cases in point include unilateral support for Israel by the Pacific territories of Palau and the Marshall Islands. This is despite there being a non-existent Jewish population in either country.   Another case is support by the Pacific island of Nauru for the Russian satellite statelets of Abkhazia and South Ossetia, which the international community regards as parts of the Eastern European country of Georgia. In this case, Russia gave Nauru a grant of $50 million in development aid in return for support. 
Beijing or Taipei?
The most notable case of chequebook diplomacy is China, as in whether you mean either the People’s Republic of China with its government based in Beijing or the Republic of China with its government based in Taipei on the island of Taiwan. Knowing that they can take advantage of the tussle between the two states, countries court them both for favourable funds in return for recognizing one of them as the legitimate country called China.
Back in the 1970s when the People's Republic of China came in from the cold and started to establish relations with most Western countries, this caused many countries to switch recognition from Taipei to Beijing. However, many other countries especially ones with authoritarian governments in the Americas, Africa and the Pacific still claimed loyalty to the government in Taipei, which was itself a dictatorship, out of the fear that if they supported the PRC, it would encourage communism in their own countries. However, in the 1990s when such possibilities seemed highly unlikely, some changed their recognition, such as South Korea in 1992.
Nevertheless, there were some countries still sticking to loyalty to Taipei, so Beijing started to offer aid and later cheap loans as an incentive to change allegiance. This later started a tit-for-tat situation where Taipei offered more money for loyalty, and so on and so on. One case is eSwatini. Despite the ending of recognition by Burkina Faso in 2018, virtually every other country in Africa supports recognition of Beijing. But not eSwatini, it still supports Taiwan and has an embassy in the capital.
When things go south
One of the problems of chequebook diplomacy is that countries become over-reliant over it, from both the donor and the receiver. And when things go sour between both nations, this leads to all kinds of problems. Venezuela was heavily reliant on it to prop-up diplomatic relations between itself and other countries in Latin America, principally to support its viewpoints such as Union of South American Nations and Bolivarian Alliance for the Americas. When the Venezuelan economy tanked, much of its support fizzled away.
When Fiji received a donation of over $30 million worth of arms from Russia, which causes concern from other Pacific countries including Australia and New Zealand. This is because the country had two military coups in 1987 and 2002, and was worried about a possible inter-ethnic conflict between the country's indigenous population and its large South Asian minority. Also, there were concerns that Russia was trying to turn Fiji into a client state of Russia.  
There has been uneasiness about much of the aid and loans that Beijing is giving to many countries throughout the global South, especially since they require very little oversight and accountability in the way they are put out. Plus, when relations go sour between China and the recipient such as recently with Sri Lanka, China may start charge higher interest payments or demand that the loan is paid imminently and often using any work that China has done as collateral.  This has been called “debt-trap diplomacy”.
- "Israel at the ends of the Earth", Tablet Magazine
- Durando, Jessica, Dorell, Oren; "Here are the 7 small nations that sided with U.S. and Israel on U.N.'s Jerusalem vote", USA Today
- Harding, Luke; "Tiny Nauru struts world stage by recognizing breakaway republics", The Guardian
- "eSwatini and Taiwan: global diplomacy’s odd couple" The Week
- Embassy of the Kingdom of Swaziland to the Republic of China on Taiwan (Taipei)
- Doherty, Ben; Secret Russian arms donation to Fiji raises concerns of bid for Pacific influence, The Guardian
- Concerns over use of Russian arms by Fiji Radio New Zealand
- Abi-Habib, Maria; How China Got Sri Lanka to Cough Up a Port The New York Times