ITIL is a globally recognized framework for ITSM (IT Service Management). It was originally developed in the UK in the 80s, and after multiple iterations has evolved into one of the most widely accepted set of guidelines for ITSM.
AXELOS – the organization that owns ITIL – describes it as:

The most widely accepted approach to IT service management in the world. ITIL can help individuals and organizations use IT to realize business change, transformation and growth.

The ITIL framework consists of 5 stages

Service Strategy

Service Strategy is the planning and getting ready for that the service provider needs to do to deliver services that meet business needs.

Strategy Management for IT Services

The objective of this process is to assess the service provider’s offerings, capabilities, competitors and market space to develop a strategy to serve its customers. Once the strategy is in place, this process is also responsible for ensuring its implementation. This process is owned by the Service Strategy Manager.

Service Portfolio Management

ITIL Service Portfolio Management, as the name suggests, is responsible for managing the service portfolio. This process ensures that the service provider has the right mix of services to meet required business outcomes at an appropriate level of investment. This process is owned by the Service Portfolio Manager.

Demand Management

The objective of ITIL Demand Management is to understand, anticipate, and influence customer demand for services. This process works with Capacity Management to ensure that the service provider has sufficient capacity to meet the required demand for particular services. This process is owned by the Demand Manager.

Business Relationship Management

ITIL Business Relationship Management (BRM) aims to maintain a positive relationship between the business and its customers. The BRM process identifies the needs of existing and potential customers and ensures that appropriate services are developed to meet those needs. This process is owned by the Business Relationship Manager.

Financial Management for IT Services

This process aims to manage the service provider's budgeting, accounting, and charging requirements. It’s owned by the Financial Manager.

Service Design

It’s the design of everything required to deliver a service, from the service through to management.

Design Coordination

The objective of ITIL Design Coordination is to coordinate all service design activities, processes and resources. This process ensures the consistent and effective design of new or changed IT services, service management information systems, architectures, technology, processes, information, and metrics. This process is owned by the Service Design Manager.

Service Level Management

Service Level Management is responsible for maintaining the IT Organization's Service Catalog and reaching binding agreements for internal and external Service Performances. Service Level Agreements are agreed upon after meetings with the clients. The Service Level Manager is responsible for the monitoring of the agreed quality parameters and suggest counter-measures when necessary. This process is owned by the Service Level Manager.

Service Catalog Management

ITIL Service Catalog Management aims to ensure that a Service Catalog is produced and maintained. It’s also responsible for maintaining accurate information on all operational services and those being prepared to be run operationally. This process provides vital information for all other ITIL service management processes: service details, current status and the services' interdependencies. This process is owned by the Service Catalog Manager.

Availability Management

The objective of ITIL Availability Management is to define, analyze, plan, measure, and improve all aspects of the availability of IT services. It’s responsible for ensuring that all IT infrastructure, processes, tools, roles etc. are appropriate for the agreed upon availability targets. This process is owned by the Availability Manager.

Capacity Management

ITIL Capacity Management aims to ensure that the capacity of IT services and the IT infrastructure is able to deliver the agreed upon service level targets in a cost effective and timely manner. This process considers all resources required to deliver the IT service, and plans for the fulfilment of short, medium and long term business requirements. This process is owned by the Capacity Manager.

Supplier Management

ITIL Supplier Management aims to ensure that all contracts with suppliers support the needs of the business. This process is also responsible for making sure that all suppliers meet their contractual commitments. This process is owned by the Supplier Manager.

IT Service Continuity Management

IT Service Continuity Management (ITSCM) aims to manage risks that could seriously impact IT services. This process ensures that the IT service provider can always provide minimum agreed upon Service Levels, by reducing the risk from disaster events to an acceptable level and planning for the recovery of IT services. ITSCM should be designed to support Business Continuity Management. This process is owned by the IT Service Continuity Manager.

Information Security Management

Information Security (InfoSec) describes activities needed for the protection of information and information infrastructure assets against the risks of loss, misuse, disclosure, or damage. Information Security Management (ISM) describes controls that an organization needs to implement to ensure that it is sensibly managing these risks. This process is owned by the Information Security Manager.

Service Transition

This stage covers introducing, changing, and retiring services. The constituent processes include

Transition Planning and Support

The objective of ITIL Project Management is to plan and coordinate the resources to deploy a major Release within the predicted cost, time, and quality estimates. This process is owned by the Project Manager.

Change Evaluation

ITIL Change Evaluation aims to assess major changes (like the introduction of a new service or a substantial change to an existing service) before they proceed to the next phase of their lifecycle. This process is owned by the Change Manager.

Change Management

ITIL Change Management controls the lifecycle of all changes. The primary objective of this process is to enable beneficial changes to be made with minimum disruption to IT services. This process is owned by the Change Manager.

Release and Deployment Management

This process aims to plan, schedule and control the movement of releases to test and live environments. The primary goal of Release and Deployment Management is to ensure that the integrity of the live environment is protected and that the correct components are released. This process is owned by the Release Manager.

Service Validation and Testing

ITIL Service Validation and Testing aims to ensure that deployed Releases and the resulting services meet customer expectations. This process verifies that IT operations is able to support the new service. This process is owned by the Test Manager.

Asset and Configuration Management

The objective of ITIL Service Asset and Configuration Management is to maintain information about Configuration Items (CIs) required to deliver an IT service, including their relationships with one another. This process is owned by the Configuration Manager.

Knowledge Management

ITIL Knowledge Management aims to gather, analyze, store and share knowledge and information within an organization. The primary purpose of this ITIL process is to ensure that appropriate knowledge is available to everyone whenever they need it. It improves efficiency by reducing the need to rediscover knowledge. This process is owned by the Knowledge Manager.

Service Operation

Service Operation is where the service desk, and its activities, sits. Constituent processes include:

Event Management

The objective of ITIL Event Management is to make sure services and CIs are constantly monitored. This process aims to filter and categorize Events in order to make sense of them and suggest appropriate action if required. This process is owned by the IT Operations Manager.

Incident Management

Incident Management aims to manage the lifecycle of all Incidents (unplanned interruptions or reductions in quality of IT services). The primary objective of this process is to return the IT service to users as quickly as possible. This process is owned by the Incident Manager.

Problem Management

Problem Management aims to manage the lifecycle of all Problems. The primary objectives of this process are to prevent Incidents from happening, and to minimize the impact of incidents that cannot be prevented. This is done by finding workarounds and permanent solutions via root cause analysis. 'Proactive Problem Management' analyzes Incident records, and uses data collected by other ITSM processes to identify trends or significant Problems. This process is owned by the Problem Manager.

Access Management

The objective of Access Management is to grant authorized users the right to use a service, while preventing access to non-authorized users. This process essentially executes policies defined in Information Security Management. Access Management is sometimes also referred to as 'Rights Management' or 'Identity Management'. This process is owned by the Access Manager.

Request Fulfilment

This process aims to fulfill Service Requests, which in most cases are minor (standard) Changes (like a password reset request or a request for information). This process is owned by the Incident Manager.

Continual service improvement (CSI)

CSI is all about improvement. Although it’s technically one of the phases of the service lifecycle, it is more of a mindset that integrates throughout the lifecycle. In order to achieve the maximum benefit that CSI can potentially offer, you’ll need to cultivate a culture of continuous improvement in your IT organization. This is done by measuring and constantly monitoring the KPIs (Key Performance Indicators) and identifying opportunities for improvement. These improvements might be triggered by a change in the business strategy or operational inefficiencies that might be draining resources. CSI aims to improve the overall effectiveness and efficiency of IT services and processes.