You can use this REST API to gather basic info from the blockchain

This is the currently officially supported API to explore Cardano transactions. In future it may be augmented or replaced by cardano-graphql, but cardano-explorer-api will be supported for some time, even once alternatives become available.

You can use this REST API to send signed-transactions to the blockchain

This is the currently officially supported API to submit signed Cardano transactions to the blockchain.

You can use this GraphQL API to gather composed info from the blockchain

GraphQL is a query language and execution environment with server and client implementations across many programming languages. The language can be serialized for network transmission, schema implementations hashed for assurance, and is suited for describing most domains. Cardano project is implementing a GraphQL API, to make exploring blockchain data a breeze.

You can use this JSON-WSP (websocket) API to gather live blockchain info directly from a cardano-node instance

Ogmios is a translation service written in Haskell running on top of cardano-node. It offers a JSON-WSP interface through WebSockets and enables clients to speak Ouroboros' mini-protocols via remote procedure calls over JSON.

You can use this REST API to perform SQL queries to gather info from the blockchain

Cardano DB Sync is to follow the Cardano chain and take information from the chain and an internally maintained copy of ledger state. Data is then extracted from the chain and inserted into a PostgreSQL database that can be accessed through a read-only REST API exposed by an instance of the postgREST project.

Cardano implementation for the Rosetta open-source specification.

Rosetta is an open-source specification and set of tools that makes integrating with blockchains simpler, faster, and more reliable.

You can use this REST API to setup a local socket file and use cardano-cli against it

cardano-cli is the first class citizen supporting every new blockchain feature, and this endpoint helps to transport a cardano-node's socket to you using a secure HTTPS tunnel. Currently access to this API is enabled on demand. Authorization and secure channel is setup with https://github.com/jpillora/chisel and TCP-to-socket termination can be done by using `socat`