Whether the state collects zakat is the question that most separates Muslim countries from one another, and it has consequences well beyond the religious.
The classical arrangement was collection by the ruler, and several modern states have restored some version of it: Saudi Arabia, Pakistan, Sudan, Libya, Yemen and Malaysia levy it in some form, though the scope differs greatly between them. Pakistan's compulsory deduction from bank accounts prompted a formal exemption for Shia Muslims, who dispute the state's authority to collect it at all, which is an instructive example of how an apparently simple obligation interacts with sect and with the machinery of a modern state.
Most Muslim-majority countries do not compel payment. It is voluntary and moves through mosques, national zakat foundations, and increasingly through applications that calculate a person's liability from their account balances and disburse it on their behalf. The annual total is very large and genuinely hard to measure, because much of it is given directly and privately, which is what the tradition recommends; figures in the tens of billions of dollars are commonly cited and should be treated as estimates rather than as accounting.
There is a live argument about effectiveness. Because zakat must reach individuals in named categories, it suits direct relief and sits awkwardly with long-term development work, which funds institutions rather than people. Islamic finance scholarship has spent considerable effort on whether building a school or a clinic can qualify, and the disagreement is real and unresolved. Meanwhile the international humanitarian sector has become interested in zakat as a funding stream, and several United Nations agencies now run zakat funds with formal rulings from Muslim scholars certifying that they comply.