Some missing types in axios for NodeJS (types would be different in browser).

global.d.ts

import axios from 'axios';
import { IncomingMessage } from 'http';

// browser version would use Uint8Array instead of Buffer and woudln't have stream/IncomingMessage
// since Buffer is a sub-class of Uint8Array you could use that in nodejs too, if you don't need any of the Buffer specific methods
declare module 'axios' {
    interface AxiosInstance {
        request(config: AxiosRequestConfig & { responseType: 'arraybuffer' }): Promise<AxiosResponse<Buffer>>;
        request(config: AxiosRequestConfig & { responseType: 'text' }): Promise<AxiosResponse<string>>;
        request(config: AxiosRequestConfig & { responseType: 'stream' }): Promise<AxiosResponse<IncomingMessage>>;

        get(url: string, config?: AxiosRequestConfig & { responseType: 'arraybuffer' }): Promise<AxiosResponse<Buffer>>;
        get(url: string, config?: AxiosRequestConfig & { responseType: 'text' }): Promise<AxiosResponse<string>>;
        get(url: string, config?: AxiosRequestConfig & { responseType: 'stream' }): Promise<AxiosResponse<IncomingMessage>>;

        delete(url: string, config?: AxiosRequestConfig & { responseType: 'arraybuffer' }): Promise<AxiosResponse<Buffer>>;
        delete(url: string, config?: AxiosRequestConfig & { responseType: 'text' }): Promise<AxiosResponse<string>>;
        delete(url: string, config?: AxiosRequestConfig & { responseType: 'stream' }): Promise<AxiosResponse<IncomingMessage>>;

        head(url: string, config?: AxiosRequestConfig & { responseType: 'arraybuffer' }): Promise<AxiosResponse<Buffer>>;
        head(url: string, config?: AxiosRequestConfig & { responseType: 'text' }): Promise<AxiosResponse<string>>;
        head(url: string, config?: AxiosRequestConfig & { responseType: 'stream' }): Promise<AxiosResponse<IncomingMessage>>;

        options(url: string, config?: AxiosRequestConfig & { responseType: 'arraybuffer' }): Promise<AxiosResponse<Buffer>>;
        options(url: string, config?: AxiosRequestConfig & { responseType: 'text' }): Promise<AxiosResponse<string>>;
        options(url: string, config?: AxiosRequestConfig & { responseType: 'stream' }): Promise<AxiosResponse<IncomingMessage>>;

        post(url: string, data?: any, config?: AxiosRequestConfig & { responseType: 'arraybuffer' }): Promise<AxiosResponse<Buffer>>;
        post(url: string, data?: any, config?: AxiosRequestConfig & { responseType: 'text' }): Promise<AxiosResponse<string>>;
        post(url: string, data?: any, config?: AxiosRequestConfig & { responseType: 'stream' }): Promise<AxiosResponse<IncomingMessage>>;

        put(url: string, data?: any, config?: AxiosRequestConfig & { responseType: 'arraybuffer' }): Promise<AxiosResponse<Buffer>>;
        put(url: string, data?: any, config?: AxiosRequestConfig & { responseType: 'text' }): Promise<AxiosResponse<string>>;
        put(url: string, data?: any, config?: AxiosRequestConfig & { responseType: 'stream' }): Promise<AxiosResponse<IncomingMessage>>;

        patch(url: string, data?: any, config?: AxiosRequestConfig & { responseType: 'arraybuffer' }): Promise<AxiosResponse<Buffer>>;
        patch(url: string, data?: any, config?: AxiosRequestConfig & { responseType: 'text' }): Promise<AxiosResponse<string>>;
        patch(url: string, data?: any, config?: AxiosRequestConfig & { responseType: 'stream' }): Promise<AxiosResponse<IncomingMessage>>;
    }
}